From Combinatorics to Dynamical Systems
Title | From Combinatorics to Dynamical Systems PDF eBook |
Author | Frederic Fauvet |
Publisher | Walter de Gruyter |
Pages | 257 |
Release | 2008-08-22 |
Genre | Mathematics |
ISBN | 3110200007 |
This volume contains nine refereed research papers in various areas from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered include irregular connections, rank reduction and summability of solutions of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi-polynomial formalism, Padé approximants related to analytic integrability, hybrid systems. The interactions between computer algebra, dynamical systems and combinatorics discussed in this volume should be useful for both mathematicians and theoretical physicists who are interested in effective computation.
An Introduction to Sequential Dynamical Systems
Title | An Introduction to Sequential Dynamical Systems PDF eBook |
Author | Henning Mortveit |
Publisher | Springer Science & Business Media |
Pages | 261 |
Release | 2007-11-27 |
Genre | Mathematics |
ISBN | 0387498796 |
This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.
Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics
Title | Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics PDF eBook |
Author | Sébastien Ferenczi |
Publisher | Springer |
Pages | 434 |
Release | 2018-06-15 |
Genre | Mathematics |
ISBN | 3319749080 |
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.
Combinatorial Dynamics And Entropy In Dimension One
Title | Combinatorial Dynamics And Entropy In Dimension One PDF eBook |
Author | Alseda Luis |
Publisher | World Scientific Publishing Company |
Pages | 344 |
Release | 1993-06-04 |
Genre | Mathematics |
ISBN | 9814553220 |
In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy
Combinatorics, Words and Symbolic Dynamics
Title | Combinatorics, Words and Symbolic Dynamics PDF eBook |
Author | Valérie Berthé |
Publisher | Cambridge University Press |
Pages | 496 |
Release | 2016-02-26 |
Genre | Computers |
ISBN | 1107077028 |
Surveys trends arising from the applications and interactions between combinatorics, symbolic dynamics and theoretical computer science.
Representation Theory, Dynamical Systems, and Asymptotic Combinatorics
Title | Representation Theory, Dynamical Systems, and Asymptotic Combinatorics PDF eBook |
Author | V. Kaimanovich |
Publisher | American Mathematical Soc. |
Pages | 258 |
Release | 2011-11-09 |
Genre | Mathematics |
ISBN | 0821872893 |
This volume, devoted to the 70th birthday of the well-known St. Petersburg mathematician A. M. Vershik, contains a collection of articles by participants in the conference "Representation Theory, Dynamical Systems, and Asymptotic Combinatorics", held in St. Petersburg in June of 2004. The book is suitable for graduate students and researchers interested in combinatorial and dynamical aspects of group representation theory.
Combinatorial Constructions in Ergodic Theory and Dynamics
Title | Combinatorial Constructions in Ergodic Theory and Dynamics PDF eBook |
Author | A. B. Katok |
Publisher | American Mathematical Soc. |
Pages | 127 |
Release | 2003 |
Genre | Mathematics |
ISBN | 0821834967 |
Ergodic theory studies measure-preserving transformations of measure spaces. These objects are intrinsically infinite, and the notion of an individual point or of an orbit makes no sense. Still there are a variety of situations when a measure preserving transformation (and its asymptotic behavior) can be well described as a limit of certain finite objects (periodic processes). The first part of this book develops this idea systematically. Genericity of approximation in various categories is explored, and numerous applications are presented, including spectral multiplicity and properties of the maximal spectral type. The second part of the book contains a treatment of various constructions of cohomological nature with an emphasis on obtaining interesting asymptotic behavior from approximate pictures at different time scales. The book presents a view of ergodic theory not found in other expository sources. It is suitable for graduate students familiar with measure theory and basic functional analysis.