Format: Paperback / softback, 132 pages, height x width: 235x155 mm, 1 Illustrations, color
Series: SpringerBriefs in Mathematics
Pub. Date: 25-Jan-2026
ISBN-13: 9783032088680
This book provides an overview of recent advances in fixed-point theory for pointwise Lipschitzian semigroups of nonlinear operators, with emphasis on the asymptotic approach. It consolidates otherwise fragmented, inconsistent, and incomplete, publications surrounding the foundations of the theory of common fixed points for semigroups of nonlinear, pointwise Lipschitzian mappings acting in Banach spaces, with some pointers to the parallel results in other settings, including metric and modular spaces. The main focus of the proposed book will be on the following aspects: (1) existence results, (2) construction algorithms convergence in the strong and the weak topology, (3) stability of such algorithms, (4) applications to differential equations, dynamical systems and stochastic processes.
The main feature of this work can be described as the introduction of the common, very general and yet relatively elementary (using basic notions of the Banach space geometry) framework, which will allow the reader to comprehend the whole story, including the inner interdependencies, behind the theory of such common fixed points. As the sub-title suggests, we will use the lenses of asymptotic and pointwise asymptotic variants of nonexpansiveness. This approach, when used in a consistent way, assures generality of the results, illustrate in relatively simple terms the current stage of the research, while allowing the readers to start or continue work on further extensions and generalizations. The value of and the need for the use of the asymptotic approach will be explained from the theoretical point of view and illustrated by examples.
While the main benefit the readers should expect form this work is to get a guidebook for the fixed point theory for the asymptotic pointwise Lipschitzian semigroups, the book can be also used as a brief compendium of the common fixed point results for more classical semigroups of nonexpansive mappings, being a special case in our much more general settings. Also, and importantly, the results discussed in this work are generally proved for semigroups parametrized by any additive sub-semigroups of the set of all nonnegative real numbers, and hence can be also applied to discrete cases, including the fixed point results for asymptotic pointwise nonexpansive mapping, generalizing in this way classical results of Goebel, Kirk, Xu, and others.
Preface.- Introduction.- Preliminaries.- Semigroups of nonlinear
operators.- Existence of common fixed points for pointwise Lipschitzian
semigroups.- Construction of common fixed points.- Applications and related
topics.- Notes.- Bibliography.-Inde
Format: Hardback, height x width: 235x155 mm, Approx. 500 p.
Series: Springer Proceedings in Complexity
Pub. Date: 01-Jan-2026
ISBN-13: 9783032091000
This book encompasses a diverse array of contemporary topics in chaos theory nonlinear dynamics and applications of theirs, including theory of nonlinear dynamics, mathematical chaos, physics and astronomy, circuits and systems, memristors, complex networks, pattern formation, biological systems, time-series analysis, and the intricate behaviors of neural, psychological, psychosocial, socio-economic, and global systems. The conference serves as a platform for scientists, engineers, economists, and social scientists to come together and discuss the latest advancements and findings in the realm of nonlinear and complex (chaotic) system behavior.
The 6th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems, held from May 8 to May 10, 2025, in Istanbul, Turkey, continued a tradition of dialogue and discovery bringing together researchers, engineers, economists, and social scientists from around the globe in a shared effort to explore the latest developments and applications in nonlinear science and complexity. As expected, it expanded its scope to cover a broader range of subjects such as unconventional cryptography, physical unclonable functions, reservoir computing, and quantum information, further enriching the interdisciplinary exchange of ideas and research.
Benchmarking Polynomial Chaos Techniques for Uncertainty Propagation in
the Lorenz System: Intrusive vs Non Intrusive Approach.- High Energy States
of Recurrent Chaotic Trajectories in Time Dependent Potential Well.- Solving
the Hamiltonian Path Problem Using Transiently Chaotic Dynamical Systems.- A
Novel Mixing Method for 3D Tumbler Mixers.- Fractals and the Mandelbrot set
via iterated quantum maps.- Spectral Detection of Connectivity in
Experimental Networks Under Chaotic Regimes.- Chaos Detection in Dynamical
Systems: The Lyapunov and Reversibility Error Invariants.- From Stability to
Chaos: Fixed Points and Bifurcations in the Framework of Discrete Dynamical
Systems.- Barred Galaxies as Complex Dynamical Systems: How Order and Chaos
Shape Galactic Bars.- Complex Thermal Dynamics of Smart Cylindrical Shells
with Nanoparticles.- Chaotic Mobile Robot for Coverage Path Planning
Scenarios Using Lorenz System.- Influence of Fiber Directional Order on Pore
Formation and Spatial Statistics in Fibrous Materials.- Quantum Artificial
Intelligence: An Innovation within the Innovation.- Semidefinite Programming
Certificates for Synchronization of Kuramoto Oscillators on Arcs.- Dual
Lyapunov based Synchronization Control of Rössler System.- Organic
Electrochemical Transistors with Memristive behavior for textile knitted
circuits.- An Examination of the Effects of Thermal Stress on the Complexity
of Flash PUFs.- Chaos Based Quantification of Image Complexity.-
Investigating Hallucinations in Artificial Intelligence Based Forecasting of
Chaotic Time Series.- The Grand Strategy is Dead, Long Live the Grand
Strategy!.- The Relationship Between the Logistics Performance Index and
Economic Growth: A Panel Data-Based Analysis for the Period 2007 to 2023.-
Which Strategy Configurations Enable Turkish Firms to Reach Peaks on the
Fitness Landscape?.- Social Dynamics and Thermodynamics Mobility on Urban
Networks.- Panel Data Analysis of the Relationship Between Renewable Energy
Share and the Human Development Index.- Chaotic Dynamics in Gold Price Time
Series: A Physics Based Forecasting Approach.- Chaotic Dynamics and
Forecasting in Monthly Rate Employment Time Series: The Case of Australia,
Colombia, Greece, Turkey and USA.- Modeling Womens Employment in Turkey and
the BRICS through Fractal Analysis and Chaos Theory.- Exploring the
Assessment of Student Attention and Engagement through Computer Vision.-
Modeling Student Behavior and Predicting Academic Performance Using LMS
Data.- Sentiment Analysis on Biblical Texts.- Mapping Competency Development
Through Student Interaction Networks in a Web 3.0 Learning Environment.-
Competency Development of University Students Under VUCA Conditions: A
Qualitative Study Based on the Complex Systems Approach.- Network Analysis of
Chaotic Dynamics and Stability of Liposomal Nanosystems.- Applying Social
Network Analysis to the Eurovision Song Contest.- Bounded Confidence Opinion
Dynamics based on the Independent Cascade Model on Signed Social Networks.-
Colon Cancer Disease Diagnosis based on CNN and Machine Learning.-
Investigations of the Interactions of Glu Glu Arg, Glu Pro Arg and Pro Arg
Pro Tripeptides that have Anticancer properties with Human Serum Albumin by
Molecular Docking Studies.- Application of Machine Learning in the Drug
Development Process.- Translating Mitochondrial Complexity into Drug Delivery
Design.
Format: Hardback, 312 pages, height x width: 235x155 mm, 2 Illustrations, color; 4 Illustrations, black and white
Series: Infosys Science Foundation Series
Pub. Date: 22-Jan-2026
ISBN-13: 9789819534418
This book presents selected chapters from the program Zariski–Dense Subgroups, Number Theory, and Geometric Applications, held at the International Center for Theoretical Sciences (ICTS) in Bengaluru, Karnataka, India, from January 1–12, 2024. The program encompassed a rich array of topics centered around Zariski-dense subgroups, with connections to algebraic and Lie groups, geometry, and number theory. It highlights the application of Diophantine approximation techniques to questions on linear groups with bounded generation, as well as innovative developments in the Bruhat–Tits theory for algebraic groups over local fields. These ideas were explored through four mini-courses alongside numerous research and expository lectures.
Chapters are published in two volumes: Volume 1 features expanded notes from four mini-courses and two expository talks, while Volume 2 comprises twelve original research articles. Collectively, the volumes make recent advances in the theory of Zariski-dense subgroups accessible to a broad mathematical audience. The topic has continued to draw significant interest, building on discussions from earlier meetings such as the MSRI workshop in Berkeley (2012) and the IPAM workshop at UCLA (2015). Over the past two decades, Zariski-dense subgroups of algebraic groups have become a focal point of intense research, yielding a wealth of results with far-reaching applications. Notably, this line of inquiry has contributed to the construction of expander graphs and the study of spectral gaps, developments that culminated in the theory of superstrong approximation.
Convolution and Square in Abelian Groups III.- Some Recent Results on the Punctual Quot Schemes.- Properly Discontinuous Actions of Discrete Subgroups of Lie Groups: Lie Theory and Computational Methods.- Word Maps and Random Words.- Things We Can Learn by Considering Random Locally Symmetric Manifolds.- Affne Anosov Representations.- Congruent Elliptic Curves over Some p-adic Lie Extensions.- Rost Injectivity and Local-Global Principle for Classical Groups over Function Fields of Arithmetic Surfaces.- Relative Weyl Character Formula, Relative Pieri Formulas and Branching Rules for Classical Groups.- Totally Ramified Subfields of p-algebras over Discrete Valued Fields with Imperfect Residue.- Residual Finiteness and Discrete Subgroups of Lie Groups.- Characterization of Norm and Quasi-norm Forms in S-adic Setting.
Format: Hardback, 424 pages, height x width: 235x155 mm, X, 424 p.
Pub. Date: 25-Jan-2026
ISBN-13: 9783032089489
The aim of this volume, Functional Equations and Ulams Problem, is to publish a well-balanced collection of works devoted to the domain of functional equations with emphasis on stability results associated with Ulams problem for approximate homomorphisms. This area has been a source of active and vibrant research for more than five decades. Efforts have been made for the book to constitute a valuable reference for graduate students and advanced research scientists who wish to be introduced to the state-of-the art knowledge on the problems treated, as well as to obtain an overview of important results on stability theory, from classical to the most recent.
The contributions in this collection investigate the following topics: functional equations on a semigroup, generalized Euler-Lagrange cubic functional equations, Ulam stability results for the Davison functional equation, Hyers-Ulam stability of a pexiderized functional equation, Ulam-Hyers stability in normed spaces, Hyers-Ulam stabilities for weighted operators, stability conditions for linear functional-differential equations, semilinear functional differential equations, general bi-Jensen functional equation, norm inequalities for the Chebyshev functional in Hilbert spaces, orthogonality and generalized additive mappings in Banach modules, permuting triderivations and permuting trihomomorphisms in complex Banach algebras, bi-quadratic derivations and bi-quadratic homomorphisms in Banach algebras, novel representations of mappings, linear and affine sets and relations, and solvability relations in groupoids.
A system of cosine sine functional equations on a semigroup generated by
its squares.- Orthogonality and generalized additive mappings in Banach
modules.- General system of the generalized Euler Lagrange cubic functional
equations and stability results.- Bi hom ders in Banach algebras.- Several
New Inner Product and Norm Inequalities for the Cebysev Functional in Hilbert
Spaces.- Ulam Stability results for the Davison functional equation in 2
Banach spaces.- Ulam Stability results for the Davison functional equation in
2 Banach spaces.- Delay-Dependent Stability Conditions for Semilinear
Functional Differential Equations in a Banach Space.- General Bi Jensen
Equation and C Ternary Bi Hom Derivations on C Ternary Banach Algebras.-
Hyers Ulam Stability of a Pexiderized Functional Equation.- Impact of fixed
point theory on Ulam Hyers stability in normed spaces.- The Boundedness and
HU Stabilities for Some Weighted Operators.- Permuting triderivations and
permuting trihomomorphisms in complex Banach algebras.- C bi ternary
derivations in C algebra ternary algebras.- Lie bracket
derivation-derivations in Banach algebras.- Bi quadratic derivations and bi
quadratic homomorphisms in Banach algebras.- Representation of mapping as a
sum of mappings with familiar properties.- On Ulam stability and
hyperstability of functional equations in Banach spaces and 2 Banach spaces.-
Linear and Affine Sets and Relations.- Solvability relations in groupoids.
Format: Hardback, 476 pages, height x width: 235x155 mm, 56 Illustrations, black and white
Series: Mathematical Engineering
Pub. Date: 14-Jan-2026
ISBN-13: 9783032086334
This book is an attempt to reduce the barrier to entry for the key tools of homological algebra and develops the basic notions of homological algebra by emphasizing concrete, elementary, and computational examples in finite dimensional vector spaces. Linear algebra is the study of linear maps between vector spaces.
The broad success of linear algebra in applications is due to the dimension theorem and the algorithms that exploit it, like Gaussian elimination and QR factorizations.
Homological algebra is the study of what happens when linear maps are chained together, one after the next.
Unlike linear algebra, homological algebra is little known outside of mathematics, but is poised to become useful in engineering and data science.
The material covered in this book can be used for a one semester elementary course in computational homological algebra, but could also comfortably occupy a two-semester sequence.
This book is written for mid-division undergraduate students who have a solid background in linear algebra, but no background in abstract algebra, topology, or category theory.
Instead readers build insight by computation.
By working the examples and exercises, the requisite background material is covered as needed, and the powerful tools of homological algebra are unlocked.
Quotients of vector spaces.- Sequences and chain complexes.- Chain maps.- Abstract simplicial complexes.- Simplicial homology and homotopy.- Sequences and chain complexes of sequences.
Format: Hardback, 306 pages, height x width: 235x155 mm, 30 Illustrations, color; 15 Illustrations, black and white
Series: Trends in Mathematics
Pub. Date: 11-Jan-2026
ISBN-13: 9783032091758
This contributed volume provides an integrated perspective on modern mathematical and computational techniques for addressing complex problems in networks, control systems, learning, and game theory. It encompasses state-of-the-art research from a diverse range of disciplines, including dynamical systems, stochastic analysis, optimization, game theory, machine learning, and transportation theory. Particular emphasis is placed on connecting rigorous theoretical developments with real-world applications.
This volume is organized into twelve chapters. The first part (Chapters 1-6) addresses the optimal transportation problem in traffic networks. The second part (Chapters 7-11) investigates Markov chains with memory by examining the geometric, algebraic, dynamical, and ergodic properties of quadratic (polynomial) stochastic operators associated with cubic stochastic hypermatrices. Finally, Chapter 12 illustrates how methods from stochastic analysis and dynamical systems can be applied to lattice models of statistical mechanics defined on a Cayley tree.
Bagdasaryan, A. Geometric, Dynamic, and Stochastic Analysis of
Wardrop-Schur Optimal Transport Networks.- O'Neill, S. and Bagdasar, O.
Classical and Novel Measures for Component Criticality in Selfish-Routing
Networks.- Daher, W.; Damrah, S.; and Aydilek, H. Review of the Single-Period
Kyle Model (1985).- Dingle, K. Curious Coincidences and Kolmogorov
Complexity.- Medfouni, M.N.; Saber, M.; Korichi, K.; Marouf, N.; and Mabrouk,
E. Predicting Solid Flow and Suspended Sediment Concentrations in a Semi-Arid
Environment using Machine Learning and Deep Learning Approaches.- Azizi,
S.P.; Nafei, A.; and Hamzi, B. EDM-2DSL: Calibrated Dynamical Modeling of
Signal Decomposition Systems with Applications in Time Series Forecasting.-
Saburov, M. On Ganikhodjaev Algebra of Cubic Matrices.- Ganikhodjaev, N.
Quadratic Stochastic Operators: Ergodic Properties and Their Applications to
Evolutionary Games and Economic Models.- Ganikhodjaev, N. and Zanin, D.
Ergodic Volterra Quadratic Mappings of the Simplex.- Saburov, M.; Saburov,
K.; and Saburov, K. Global Stability of Quadratic Stochastic Operators
Associated with Column Primitive Cubic Doubly Stochastic Matrices.-
Abdushukurov, A.A.; Muradov, R.S. Stochastic Analysis of Survival Functions
Using Copulas and Its Applications.- Mukhamedov, F. and Khakimov, O. P-adic
dynamical systems fo-models on the Cayley trees.
Format: Hardback, 616 pages, height x width: 235x155 mm, 51 Illustrations, black and white
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 04-Feb-2026
ISBN-13: 9783032082664
This book provides the hitherto disregarded development of the principle of angular momentum, and aims at reconstructing its inception by analyzing Euler's relevant publications and correspondence, and using his unpublished manuscripts and notebook records. The derivation of the equations of motion for rigid body rotation is one of Euler's main achievements in mechanics and celestial mechanics. It enabled the foundation of later developments that became known as the angular momentum theorem or, as it is called here, the principle of angular momentum (PAM). Along with Euler's first mathematical formulation of Newton's law of motion, called the linear momentum theorem or the principle of linear momentum (PLM), modern historiography of science assigned these principles to Euler, honoring him by calling them Euler's principles or laws of mechanics. However, the history behind these principles, in particular the developing and establishing processes of PAM, remained in darkness until now. This is probably why Euler's achievements commonly are still subsumed in Newtonian physics or even labeled with it. A good deal of Euler's original documents relevant for unearthing these processes are presented and translated here for the first time.
Frontispiece.- Dedication.- Preface.- Acknowledgement.- Table of
Contents.- List of Figures.- List of Tables.- Abbreviations and Acronyms.-
Transcriptions of Euler's relevant publications (papers only).-
Transcriptions of Euler's relevant notebook records and manuscripts.-
Transcriptions of Euler's relevant correspondence.- References.- Name Index.-
Subject Index.- Index of Cited Documents.- Index of Cited References.
Format: Paperback / softback, 313 pages, height x width: 240x168 mm, 4 Illustrations, black and white
Series: Oberwolfach Seminars
Pub. Date: 23-Jan-2026
ISBN-13: 9783032088659
The aim of this textbook is to introduce readers at a graduate level to G-complete reducibility and explain some of its many applications across pure mathematics. It is based on the Oberwolfach Seminar of the same name which took place in 2022.
The notion of G-complete reducibility for subgroups of a reductive algebraic group is a natural generalisation of the notion of complete reducibility in representation theory. Since its introduction in the 1990s, complete reducibility has been widely studied, both as an important concept in its own right, with applications to the classification and structure of linear algebraic groups, and also as a useful tool with applications in representation theory, geometric invariant theory, the theory of buildings, and number theory.
Chapter 1. Introduction.
Chapter 2. Preliminaries.
Chapter 3. Geometric invariant theory.
Chapter 4. G-complete reducibility: first definitions and properties .
Chapter 5. The geometric approach.
Chapter 6. Finiteness, rationality and rigidity results .
Chapter 7. The spherical building of G .- 162
Chapter 8. The optimality formalism.
Chapter 9. Applications to G-complete reducibility .
Chapter 10. Large versus small characteristic .
Chapter 11. G-complete reducibility over an arbitrary field.
Chapter 12. Variations, applications and future directions .-
Chapter 13. Solutions to Exercises.- Bibiliography.-
Index.
Format: Hardback, 184 pages, height x width: 235x155 mm, 6 Illustrations, black and white
Series: Texts in Applied Mathematics
Pub. Date: 12-Jan-2026
ISBN-13: 9783032088352
Ergodic theory provides a powerful lens for understanding dynamical systems, recasting disordered and seemingly random behavior in the language of probability theory. This book offers a concise, rigorous introduction to the subject, suitable both as a graduate-level textbook and as a reference for both pure and applied mathematicians.
Part I (Chapters 1–7) lays the foundation, covering invariant measures, measure-theoretic isomorphisms, ergodicity, mixing, entropy, and culminating in the Shannon–McMillan–Breiman Theorem.
Part II (Chapters 8–13) shifts focus to continuous maps of metric spaces, exploring the collection of invariant measures corresponding to a given map.
Part III (Chapters 14–16) presents advanced topics rarely found in textbooks at this level, including SRB measures, their deep connection to entropy and Lyapunov exponents, and extensions to two important settings: random and infinite-dimensional dynamical systems.
Throughout, the authors emphasize not only the mathematical elegance of ergodic theory but also its practical relevance and rich connections to other areas of mathematics, from information theory to stochastic processes.
Measure-preserving transformations.- Three basic concepts: recurrence, ergodicity and isomorphisms.- Ergodic theorems.- A hierarchy of mixing properties.- Operations on measure-preserving transformations.- Entropy.- The Shannon-McMillan-Breiman Theorem.- Invariant measures for continuous maps.- Topological dynamics.- Lyapunov exponents.- Ingredients in the proof of the Multiplicative Ergodic Theorem.- Differentiable maps and invariant densities.- Linear operators associated to dynamical systems.- Smooth ergodic theory.- Random dynamical systems.- Infinite-dimensional dynamical systems.
Format: Hardback, 274 pages, height x width: 235x155 mm, 7 Illustrations, black and white
Series: Operator Theory: Advances and Applications
Pub. Date: 13-Jan-2026
ISBN-13: 9783032087324
This is a survey of the classical Cesąro operator aimed at graduate students as well as more experienced researchers. The eleven chapters of the book cover topics from Cesąro's early work on summability of series and continues with the seminal paper of Brown, Halmos, and Shields on the Cesąro operator.
Along the way, various normality classes of the Cesąro operator are covered, as well as invariant subspaces and semigroups. Recent and ongoing work concerning generalizations of the Cesąro operator is also included.
The book also features detailed endnotes for each chapter with historical references and suggestions for further reading.
Chapter.1.Ernesto Ces`aro.
Chapter 2.Ces`aro Summability,
Chapter 3.The Ces`aro Matrix.
Chapter 4.The Ces`aro Operator on the Space of Analytic Functions.- Chaper.5.The Ces`aro Operator on the Hardy Space.
Chapter 6.Normality Classes and the Ces`aro Operator.
Chapter 7 Fredholm Theory for the Ces`aro Operator.
Chapter 8.The Ces`aro Operator and Semigroups.
Chapter 9.Invariant Subspaces of the Ces`aro Operator.
Chapter 10.The Continuous Ces`aro Operators.
Chapter.11.Generalized Ces`aro Operators.-References.-Author Index.-Subject Index.