A Functional Approach
Author: Viviane Baladi
Publisher: Springer
ISBN: 3319776614
Category: Mathematics
Page: 291
View: 7661
The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.
Positive Transfer Operators and Decay of Correlations
Author: Viviane Baladi
Publisher: World Scientific
ISBN: 9814496669
Category: Science
Page: 324
View: 7237
Real and Complex Dynamical Systems
Author: B. Branner,Poul Hjorth
Publisher: Springer Science & Business Media
ISBN: 9401584397
Category: Mathematics
Page: 348
View: 3266
Introduction to the Modern Theory of Dynamical Systems
Author: Anatole Katok,Boris Hasselblatt
Publisher: Cambridge University Press
ISBN: 9780521575577
Category: Mathematics
Page: 802
View: 6038
Classical Nonintegrability, Quantum Chaos
Author: Andreas Knauf,Yakov G. Sinai
Publisher: Birkhäuser
ISBN: 3034889321
Category: Science
Page: 102
View: 9932
Geometric and Probabilistic Structures in Dynamics
Workshop on Dynamical Systems and Related Topics in Honor of Michael Brin on the Occasion of His 60th Birthday, March 15-18, 2008, University of Maryland, College Park, MD
Author: Michael Brin
Publisher: American Mathematical Soc.
ISBN: 0821842862
Category: Mathematics
Page: 340
View: 2582
This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications.
Author: Michael Brin
Publisher: American Mathematical Soc.
ISBN: 0821842862
Category: Mathematics
Page: 340
View: 2582
Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval
Author: David Ruelle
Publisher: American Mathematical Soc.
ISBN: 9780821836019
Category: Mathematics
Page: 62
View: 7052
Zeta Functions of Graphs
A Stroll through the Garden
Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 1139491784
Category: Mathematics
Page: N.A
View: 6618
Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.
Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 1139491784
Category: Mathematics
Page: N.A
View: 6618
Admissibility and Hyperbolicity
Author: Luís Barreira,Davor Dragičević,Claudia Valls
Publisher: Springer
ISBN: 3319901109
Category: Mathematics
Page: 145
View: 4347
Algebraic Theory of Locally Nilpotent Derivations
Author: Gene Freudenburg
Publisher: Springer
ISBN: 3662553503
Category: Mathematics
Page: 319
View: 4157
Sequences, Groups, and Number Theory
Author: Valérie Berthé,Michel Rigo
Publisher: Birkhäuser
ISBN: 331969152X
Category: Mathematics
Page: 578
View: 2544
Energy Markets and Responsive Grids
Modeling, Control, and Optimization
Author: Sean Meyn,Tariq Samad,Ian Hiskens,Jakob Stoustrup
Publisher: Springer
ISBN: 1493978225
Category: Science
Page: 518
View: 807
This volume consists of selected essays by participants of the workshop Control at Large Scales: Energy Markets and Responsive Grids held at the Institute for Mathematics and its Applications, Minneapolis, Minnesota, U.S.A. from May 9-13, 2016. The workshop brought together a diverse group of experts to discuss current and future challenges in energy markets and controls, along with potential solutions. The volume includes chapters on significant challenges in the design of markets and incentives, integration of renewable energy and energy storage, risk management and resilience, and distributed and multi-scale optimization and control. Contributors include leading experts from academia and industry in power systems and markets as well as control science and engineering. This volume will be of use to experts and newcomers interested in all aspects of the challenges facing the creation of a more sustainable electricity infrastructure, in areas such as distributed and stochastic optimization and control, stability theory, economics, policy, and financial mathematics, as well as in all aspects of power system operation.
Author: Sean Meyn,Tariq Samad,Ian Hiskens,Jakob Stoustrup
Publisher: Springer
ISBN: 1493978225
Category: Science
Page: 518
View: 807
The Riemann Legacy
Riemannian Ideas in Mathematics and Physics
Author: Krzysztof Maurin
Publisher: Springer Science & Business Media
ISBN: 9401589399
Category: Mathematics
Page: 719
View: 7447
very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum).
Author: Krzysztof Maurin
Publisher: Springer Science & Business Media
ISBN: 9401589399
Category: Mathematics
Page: 719
View: 7447
Spherical Sampling
Author: Willi Freeden,M. Zuhair Nashed,Michael Schreiner
Publisher: Birkhäuser
ISBN: 3319714589
Category: Mathematics
Page: 596
View: 9501
Interpolation Spaces
An Introduction
Author: J. Bergh,Jorgen Lofstrom
Publisher: Springer Science & Business Media
ISBN: 3642664512
Category: Mathematics
Page: 207
View: 6293
The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.
Author: J. Bergh,Jorgen Lofstrom
Publisher: Springer Science & Business Media
ISBN: 3642664512
Category: Mathematics
Page: 207
View: 6293
Handbook of Floating-Point Arithmetic
Author: Jean-Michel Muller,Nicolas Brunie,Florent de Dinechin,Claude-Pierre Jeannerod,Mioara Joldes,Vincent Lefèvre,Guillaume Melquiond,Nathalie Revol,Serge Torres
Publisher: Birkhäuser
ISBN: 3319765264
Category: Mathematics
Page: 627
View: 5019
Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness
Author: Hubert Hennion,Loic Herve
Publisher: Springer
ISBN: 3540446230
Category: Mathematics
Page: 152
View: 795
Computational Invariant Theory
Author: Harm Derksen,Gregor Kemper
Publisher: Springer
ISBN: 3662484226
Category: Mathematics
Page: 366
View: 5189
Spectral Theory of Infinite-Area Hyperbolic Surfaces
Author: David Borthwick
Publisher: Birkhäuser
ISBN: 3319338773
Category: Mathematics
Page: 463
View: 5761
Analytic Number Theory, Modular Forms and q-Hypergeometric Series
In Honor of Krishna Alladi's 60th Birthday, University of Florida, Gainesville, March 2016
Author: George E. Andrews,Frank Garvan
Publisher: Springer
ISBN: 3319683764
Category: Mathematics
Page: 736
View: 463
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Author: George E. Andrews,Frank Garvan
Publisher: Springer
ISBN: 3319683764
Category: Mathematics
Page: 736
View: 463