Topological and Ergodic Theory of Symbolic Dynamics - Henk Bruin

Topological and Ergodic Theory of Symbolic Dynamics

(Autor)

Buch | Hardcover
460 Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-6984-9 (ISBN)
139,95 inkl. MwSt
Introduces symbolic dynamics from a perspective of topological dynamical systems. After introducing symbolic and topological dynamics, the core of the book consists of discussions of subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and the ergodic properties of these systems.
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples.

After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $/mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy).

The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.

Henk Bruin, University of Vienna, Austria.

First examples and general properties of subshifts
Topological dynamics
Subshifts of positive entropy
Subshifts of zero entropy
Further minimal Cantor systems
Methods from ergodic theory
Automata and linguistic complexity
Miscellaneous background topics
Solutions to exercises
Bibliography
Index

Erscheinungsdatum
Reihe/Serie Graduate Studies in Mathematics
Verlagsort Providence
Sprache englisch
Maße 178 x 254 mm
Gewicht 272 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 1-4704-6984-7 / 1470469847
ISBN-13 978-1-4704-6984-9 / 9781470469849
Zustand Neuware
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