000			01774nam a22001697a 4500
003			OSt
005			20240301150811.0
008			240301b |||||||| |||| 00| 0 eng d
020			_a9781470472191
100			_aBruin, Henk
245			_aTopological and Ergodic Theory of Symbolic Dynamics/ _cHenk Bruin
260			_aProvidence, Rhode Island: _bAmerican Mathematical Society, _c2022.
300			_axvii,461p.
490			_aGraduate Studies in Mathematics 228
520			_aSymbolic 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.
942			_2ddc _cBK
999			_c23061 _d23061