Geometric and Probabilistic Aspects
Provides a self-contained introduction to the theory of Young towers for
dynamical systems with inducing schemes
Collects recent results on nonuniformly expanding maps and partially
hyperbolic diffeomorphisms
Includes a detailed account of Gibbs?Markov maps
This monograph offers a coherent, self-contained account of the theory of Sinai?Ruelle?Bowen
measures and decay of correlations for nonuniformly hyperbolic dynamical systems. A central
topic in the statistical theory of dynamical systems, the book in particular provides a detailed
exposition of the theory developed by L.-S. Young for systems admitting induced maps with
certain analytic and geometric properties. After a brief introduction and preliminary results,
Chapters 3, 4, 6 and 7 provide essentially the same pattern of results in increasingly
interesting and complicated settings. Each chapter builds on the previous one, apart from
Chapter 5 which presents a general abstract framework to bridge the more classical expanding
and hyperbolic systems explored in Chapters 3 and 4 with the nonuniformly expanding and
partially hyperbolic systems described in Chapters 6 and 7. Throughout the book, the theory is
illustrated with applications. A clear and detailed account of topics of current research interest,
this monograph will be of interest to researchers in dynamical systems and ergodic theory. In
particular, beginning resea
Due 2021-02-08
1st ed. 2020, XIII, 259 p. 5 illus.
Hardcover
ISBN 978-3-030-62813-0
Product category :Monograph
Series : Springer Monographs in Mathematics
Mathematics : Dynamical Systems and Ergodic Theory
Focuses on the fundamentals of fractional calculus of fractal functions in
various settings, and its applications in signal analysis
Covers thoroughly the generalized fractal dimensions and the discrete
wavelet transform for analyzing EEG signals
Discusses the fuzzy multifractal dimensions for analyzing the mathematical
and clinical waveforms
This book introduces the fractal interpolation functions (FIFs) in approximation theory to the
readers and the concerned researchers in advanced level. FIFs can be used to precisely
reconstruct the naturally occurring functions when compared with the classical interpolants.
The book focuses on the construction of fractals in metric space through various iterated
function systems. It begins by providing the Mathematical background behind the fractal
interpolation functions with its graphical representations and then introduces the fractional
integral and fractional derivative on fractal functions in various scenarios. Further, the existence
of the fractal interpolation function with the countable iterated function system is
demonstrated by taking suitable monotone and bounded sequences. It also covers the
dimension of fractal functions and investigates the relationship between the fractal dimension
and the fractional order of fractal interpolation functions. Moreover, this book explores the idea
of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the
problems of identification of the characterizing parameters. In the application section, this
research compendium addresses the signal processing and its Mathematical methodologies. A
wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals
contaminated by nonstationary noises is presented, and the author investigates the recognition
of healthy, epileptic EEG and cardiac ECG signals using multifractal measures.
Due 2021-01-29
1st ed. 2021, X, 133 p. 61 illus., 60 illus. in color.
Hardcover
ISBN 978-3-030-62671-6
Product category : Monograph
Series : Understanding Complex Systems
Physics : Applications of Nonlinear Dynamics and Chaos Theory
Maximum and Compact Support Principles and Detours on Manifolds
Investigates the validity of strong maximum principles, compact support
principles and Liouville type theorems
Aims to give a unified view of recent results in the literature
This book demonstrates the influence of geometry on the qualitative behaviour of solutions of
quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from
the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities
on domains of a manifold M with very general nonlinearities depending on the variable x, on
the solution u and on its gradient. The book highlights the mean curvature operator and its
variants, and investigates the validity of strong maximum principles, compact support principles
and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or
volume growth of geodesic balls in M to guarantee the above properties under appropriate
Keller-Osserman type conditions, which are investigated in detail throughout the book, and
discusses the geometric reasons behind the existence of such thresholds. Further, the book
also provides a unified review of recent results in the literature, and creates a bridge with
geometry by studying the validity of weak and strong maximum principles at infinity, in the
spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Due 2021-02-14
1st ed. 2020, X, 230 p.
Softcover
ISBN 978-3-030-62703-4
Product category : Monograph
Series : Frontiers in Mathematics
Mathematics : Global Analysis and Analysis on Manifolds
The book displays the research and activities of Australia's international and
residential mathematics research institute, MATRIX
Contains articles on hot topics in the ten programs held at MATRIX in 2019
and the two programs held in January 2020
Top-level science from Australia
MATRIX is Australia’s international and residential mathematical research institute. It facilitates
new collaborations and mathematical advances through intensive residential research
programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held
at MATRIX in 2019 and the two programs held in January 2020: ・Topology of Manifolds:
Interactions Between High and Low Dimensions ・Australian-German Workshop on Differential
Geometry in the Large ・Aperiodic Order meets Number Theory ・Ergodic Theory, Diophantine
Approximation and Related Topics ・Influencing Public Health Policy with Data-informed
Mathematical Models of Infectious Diseases ・International Workshop on Spatial Statistics
・Mathematics of Physiological Rhythms ・Conservation Laws, Interfaces and Mixing ・Structural
Graph Theory Downunder ・Tropical Geometry and Mirror Symmetry ・Early Career Researchers
Workshop on Geometric Analysis and PDEs ・Harmonic Analysis and Dispersive PDEs: Problems
and Progress The articles are grouped into peer-reviewed contributions and other contributions.
The peer-reviewed articles present original results or reviews on a topic related to the MATRIX
program; the remaining contributions are predominantly lecture notes or short articles based
on talks or activities at MATRIX.
Due 2021-02-14
1st ed. 2020, XLI, 768 p.
176 illus. In 2 volumes, not available separately.
Hardcover
ISBN 978-3-030-62496-5
Product category : Contributed volume
Series : MATRIX Book Series
Mathematics : Mathematics (general)
A Concise Study Companion and Guide
Provides a detailed, thorough, and comprehensive review of concepts in
discrete mathematics and graph theory
Includes an introductory chapter on algorithms, and presents numerous
concepts using algorithmic notation, where applicable
Accessible enough to serve as a quick reference even for undergraduate
students of disciplines other than computer science
This textbook can serve as a comprehensive manual of discrete mathematics and graph theory
for non-Computer Science majors; as a reference and study aid for professionals and
researchers who have not taken any discrete math course before. It can also be used as a
reference book for a course on Discrete Mathematics in Computer Science or Mathematics
curricula. The study of discrete mathematics is one of the first courses on curricula in various
disciplines such as Computer Science, Mathematics and Engineering education practices.
Graphs are key data structures used to represent networks, chemical structures, games etc.
and are increasingly used more in various applications such as bioinformatics and the Internet.
Graph theory has gone through an unprecedented growth in the last few decades both in
terms of theory and implementations; hence it deserves a thorough treatment which is not
adequately found in any other contemporary books on discrete mathematics, whereas about
40% of this textbook is devoted to graph theory. The text follows an algorithmic approach for
discrete mathematics and graph problems where applicable, to reinforce learning and to show
how to implement the concepts in real-world applications.
Due 2021-02-08
1st ed. 2021, XV, 329 p. 164 illus.
Softcover
ISBN 978-3-030-61114-9
Product category : Graduate/advanced undergraduate textbook
Series : Undergraduate Topics in Computer Science
Computer Science : Discrete Mathematics in Computer Science