Format: Hardback, 802 pages, height x width: 235x155 mm, XIII, 802 p.
Pub. Date: 06-Aug-2022
ISBN-13: 9783031019715
Dynamical systems and the twin field ergodic theory have their roots in the qualitative theory of differential equations, developed by the great mathematician Henri Poincare, and in the kinetic theory of gases built in mathematical terms by physicists James Clerk Maxwell and Ludwig Boltzmann. Together, they aim to model, explain and predict the behavior of natural and artificial phenomena which evolve in time. For more than three decades, Marcelo Viana has been making several outstanding contributions to this area of mathematics. This volume contains a selection of his research papers, covering a wide range of topics: rigorous theory of strange attractors, physical measures, bifurcation theory, homoclinic phenomena, fractal dimensions, partial hyperbolicity, thermodynamic formalism, non-uniform hyperbolicity, interval exchange maps Teichmuller flows, and the modern theory of Lyapunov exponents. Marcelo Viana, a world leader in this field, has been the object of several academic distinctions, such as the inaugural Ramanujan prize of the International Centre for Theoretical Physics, and the Louis D. Scientific Grand Prix of the Institut de France. He is also recognized for his broad contribution to the mathematical community, in his country and region as well as in the international arena
Moduli of continuity for the Lyapunov exponents of random GL(2)-cocycles: El Hadji Yaya Tall and Marcelo Viana.- Continuity of Lyapunov exponents in the C 0 topology: Marcelo Viana and Jiagang Yang.- Continuity of Lyapunov exponents for random two-dimensional matrices: Carlos Bocker-Neto and Marcelo Viana.- Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows: Artur Avila, Marcelo Viana and Amie Wilkinson.- Holonomy invariance: rough regularity and applications to Lyapunov exponents: Artur Avila, Jimmy Santamaria and Marcelo Viana.- Extremal Lyapunov exponents: an invariance principle and applications: Artur Avila and Marcelo Viana.- Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents: Marcelo Viana.- Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture: Artur Avila and Marcelo Viana.- The Lyapunov exponents of generic volume-preserving and symplectic maps: Jairo Bochi and Marcelo Viana.- xv Contents Genericite d'exposants de Lyapunov non-nuls pour des produits deterministes de matrices [ Genericity of non-zero Lyapunov exponents for deterministic products of matrices]: Christian Bonatti, Xavier Gomez-Mont and Marcelo Viana.- Solution of the basin problem for Henon-like attractors: Michael Benedicks and Marcelo Viana.- SRB measures for partially hyperbolic systems whose central direction is mostly contracting: Christian Bonatti and Marcelo Viana.- SRB measures for partially hyperbolic systems whose central direction is mostly expanding: Jose F. Alves, Christian Bonatti and Marcelo Viana.- Multidimensional nonhyperbolic attractors: Marcelo Viana.- Strange attractors in saddle-node cycles: prevalence and globality: L.J. Diaz, J. Rocha and M. Viana.- High dimension diffeomorphisms displaying infinitely many periodic attractors: J. Palis and M. Viana.- Abundance of strange attractors: Leonardo Mora and Marcelo Viana.- List of Publications of Marcelo Viana.- List of Ph.D. Students of Marcelo Viana at IMPA.- Credits.
Format: Hardback, 221 pages, height x width: 235x155 mm,
4 Illustrations, black and white; X, 221 p. 4 illus
Series: Trends in Logic 59
Pub. Date: 13-Jul-2022
ISBN-13: 9783031042966
This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.
The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations. It includes the basics of the algebraic theory of regular varieties and the construction of Plonka sums over semilattice direct systems of algebra. The core of the book is devoted to an abstract definition of logics of left and right variable inclusion, respectively, and the authors study their semantics using the construction of Plonka sums of matrix models. The authors also cover Paraconsistent Weak Kleene logic and survey its abstract algebraic logical properties. This book is of interest to scholars of formal logic.
Chapter
1. Analyticity, Consequence, and Meaninglessness.
Chapter
2. Plonka Sums and Regular Varieties.
Chapter
3. Dualities for Regular Varieties.
Chapter
4. Logics of Left Variable Inclusion.
Chapter
5. Logics of Right Variable Inclusion.
Chapter
6. Paraconsistent Weak Kleene Logic.-
Format: Hardback, 490 pages, height x width: 235x155 mm, 3 Illustrations, color;
14 Illustrations, black and white; X, 490 p. 17 illus., 3 illus. in color
Series: Springer Optimization and Its Applications 194
Pub. Date: 09-Aug-2022
ISBN-13: 9783031045196
The quadratic binary optimization problem (QUBO) is a versatile combinatorial optimization model with a variety of applications and rich theoretical properties. Application areas of the model include finance, cluster analysis, traffic management, machine scheduling, VLSI physical design, physics, quantum computing, engineering, and medicine. In addition, various mathematical optimization models can be reformulated as a QUBO, including the resource constrained assignment problem, set partitioning problem, maximum cut problem, quadratic assignment problem, the bipartite unconstrained binary optimization problem, among others.
This book presents a systematic development of theory, algorithms, and applications of QUBO. It offers a comprehensive treatment of QUBO from various viewpoints, including a historical introduction along with an in-depth discussion of applications modelling, complexity and polynomially solvable special cases, exact and heuristic algorithms, analysis of approximation algorithms, metaheuristics, polyhedral structure, probabilistic analysis, persistencies, and related topics. Available software for solving QUBO is also introduced, including public domain, commercial, as well as quantum computing based codes.
Introduction to QUBO.- Applications and Computational Advances for Solving the QUBO Model.- Complexity and Polynomially Solvable Special Cases of QUBO.- The Boolean Quadric Polytope.- Autarkies and Persistencies for QUBO.- Mathematical Programming Models and ExactAlgorithms.- The Random QUBO.- Fast Heuristics and Approximation Algorithms.- Metaheuristic Algorithms.- The Bipartite QUBO.- QUBO Software.
Format: Hardback, 462 pages, height x width: 235x155 mm, 5 Illustrations,
black and white; VIII, 462 p. 5 illus.; 5 Illustrations, black and white; VIII, 462 p. 5 illus.
Series: Graduate Texts in Mathematics 293
Pub. Date: 15-Jul-2022
ISBN-13: 9783031009419
This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study.
After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff’s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth?death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter.
Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.
Symbol Definition List.-
1. Fourier Analysis: A Brief.-
2. Weakly Stationary Processes and their Spectral Measures.-
3. Spectral Representation of Stationary Processes.-
4. Birkhoff's Ergodic Theorem.-
5. Subadditive Ergodic Theory.-
6. An Introduction to Dynamical Systems.-
7. Markov Chains.-
8. Markov Processes with General State Space.-
9. Stopping Times and the Strong Markov Property.-
10. Transience and Recurrence of Markov Chains.-
11. Birth-Death Chains.-
12. Hitting Probabilities & Absorption.-
13. Law of Large Numbers and Invariant Probability for Markov Chains by Renewal Decomposition.-
14. The Central Limit Theorem for Markov Chains by Renewal Decomposition.-
15. Martingale Central Limit Theorem.-
16. Stationary Ergodic Markov Processes: SLLN & FCLT.-
17. Linear Markov Processes.-
18. Markov Processes Generated by Iterations of I.I.D. Maps.-
19. A Splitting Condition and Geometric Rates of Convergence to Equilibrium.-
20. Irreducibility and Harris Recurrent Markov Processes.-
21. An Extended Perron-Frobenius Theorem and Large Deviation Theory for Markov Processes.-
22. Special Topic: Applications of Large Deviation Theory.-
23. Special Topic: Associated Random Fields, Positive Dependence, FKG Inequalities.-
24. Special Topic: More on Coupling Methods and Applications.-
25. Special Topic: An Introduction to Kalman Filter.- A. Spectral Theorem for Compact Self-Adjoint Operators and Mercer's Theorem
.- B. Spectral Theorem for Bounded Self-Adjoint Operators.- C. Borel Equivalence for Polish Spaces.- D.
Hahn-Banach, Separation, and Representation Theorems in Functional Analysis.- References.- Author Index.- Subject Index.
Format: Paperback / softback, 110 pages,
height x width: 235x155 mm, X, 110 p.,
Series: SpringerBriefs in Mathematics
Pub. Date: 20-Aug-2022
ISBN-13: 9783030991234
This book provides a comprehensive survey of the Sharkovsky ordering, its different aspects and its role in dynamical systems theory and applications. It addresses the coexistence of cycles for continuous interval maps and one-dimensional spaces, combinatorial dynamics on the interval and multidimensional dynamical systems. Also featured is a short chapter of personal remarks by O.M. Sharkovsky on the history of the Sharkovsky ordering, the discovery of which almost 60 years ago led to the inception of combinatorial dynamics. Now one of cornerstones of dynamics, bifurcation theory and chaos theory, the Sharkovsky ordering is an important tool for the investigation of dynamical processes in nature. Assuming only a basic mathematical background, the book will appeal to students, researchers and anyone who is interested in the subject.
Preface.- 1 Coexistence of Cycles for Continuous Interval Maps.- 2 Combinatorial Dynamics on the Interval.- 3 Coexistence of Cycles for One-dimensional Spaces.- 4 Multidimensional Dynamical Systems.- 5 Historical Remarks.- 6 Appendix.