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Author | : Martine Queffélec |
Publisher | : Springer |
Total Pages | : 367 |
Release | : 2010-01-30 |
Genre | : Mathematics |
ISBN | : 3642112129 |
Download Substitution Dynamical Systems - Spectral Analysis Book in PDF, ePub and Kindle
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Author | : Martine Queffâelec |
Publisher | : |
Total Pages | : 376 |
Release | : 2010-09-10 |
Genre | : Differentiable dynamical systems |
ISBN | : 9783642112553 |
Download Substitution Dynamical Systems - Spectral Analysis Book in PDF, ePub and Kindle
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Author | : Martine Queffélec |
Publisher | : Springer |
Total Pages | : 252 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540480889 |
Download Substitution Dynamical Systems - Spectral Analysis Book in PDF, ePub and Kindle
Author | : Martine Queffélec |
Publisher | : |
Total Pages | : 240 |
Release | : 1987 |
Genre | : |
ISBN | : |
Download Substitution Dynamical Sysems Book in PDF, ePub and Kindle
Author | : Oscar F. Bandtlow |
Publisher | : |
Total Pages | : |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Spectral Analysis of Dynamical Systems Book in PDF, ePub and Kindle
Author | : Mahendra Nadkarni |
Publisher | : Springer Nature |
Total Pages | : 223 |
Release | : 2020-08-29 |
Genre | : Mathematics |
ISBN | : 9811562253 |
Download Spectral Theory of Dynamical Systems Book in PDF, ePub and Kindle
This book discusses basic topics in the spectral theory of dynamical systems. It also includes two advanced theorems, one by H. Helson and W. Parry, and another by B. Host. Moreover, Ornstein’s family of mixing rank-one automorphisms is given with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are also examined. Baire category theorems of ergodic theory, scattered in literature, are discussed in a unified way in the book. Riesz products are introduced and applied to describe the spectral types and eigenvalues of rank-one automorphisms. Lastly, the second edition includes a new chapter “Calculus of Generalized Riesz Products”, which discusses the recent work connecting generalized Riesz products, Hardy classes, Banach's problem of simple Lebesgue spectrum in ergodic theory and flat polynomials.
Author | : Mark Lʹvovich Agranovskiĭ |
Publisher | : American Mathematical Soc. |
Total Pages | : 278 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821836862 |
Download Complex Analysis and Dynamical Systems Book in PDF, ePub and Kindle
This book contains contributions from the participants of an International Conference on Complex Analysis and Dynamical Systems. The papers collected here are devoted to various topics in complex analysis and dynamical systems, ranging from properties of holomorphic mappings to attractors in hyperbolic spaces. Overall, these selections provide an overview of activity in analysis at the outset of the twenty-first century. The book is suitable for graduate students and researchers in complex analysis and related problems of dynamics. With this volume, the Israel Mathematical Conference Proceedings are now published as a subseries of the AMS Contemporary Mathematics series.
Author | : Shigeki Akiyama |
Publisher | : Springer Nature |
Total Pages | : 456 |
Release | : 2020-12-05 |
Genre | : Mathematics |
ISBN | : 3030576663 |
Download Substitution and Tiling Dynamics: Introduction to Self-inducing Structures Book in PDF, ePub and Kindle
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
Author | : Sébastien Ferenczi |
Publisher | : Springer |
Total Pages | : 434 |
Release | : 2018-06-15 |
Genre | : Mathematics |
ISBN | : 3319749080 |
Download Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics Book in PDF, ePub and Kindle
This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Author | : Fabien Durand |
Publisher | : Cambridge University Press |
Total Pages | : 594 |
Release | : 2022-02-03 |
Genre | : Mathematics |
ISBN | : 1108986099 |
Download Dimension Groups and Dynamical Systems Book in PDF, ePub and Kindle
This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.