BOWEN'S ENTROPY-CONJUGACY CONJECTURE IS TRUE UP TO FINITE INDEX

作者：Boyle Mike^*; Buzzi Jerome; McGoff Kevin

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143(7): 2991-2997.

DOI：10.1090/s0002-9939-2015-12491-4

• Symbolic dynamics
• subshifts of finite type
• topological entropy
• dimensional entropy
• entropy-conjugacy
• topological conjugacy
• left ideal class
• resolving maps

For a topological dynamical system (X, f), consisting of a continuous map f : X --> X, and a (not necessarily compact) set Z subset of X, Bowen (1973), defined a dimension-like version of entropy, h(X)(f, Z). In the same work, he introduced a notion of entropy-conjugacy for pairs of invertible compact systems: the systems (X, f) and (Y, g) are entropy-conjugate if there exist invariant Borel sets X' subset of X and Y' subset of Y such that h(X)(f, X \ X') < h(X)(f, X), h(Y) (g, Y \ Y') < h(Y) (g, Y), and (X', f vertical bar(X)') is topologically conjugate to (Y', g vertical bar(Y)'). Bowen conjectured that two mixing shifts of finite type are entropy-conjugate if they have the same entropy. We prove that two mixing shifts of finite type with equal entropy and left ideal class are entropy-conjugate. Consequently, in every entropy class Bowen's conjecture is true up to finite index.

• 出版日期2015-7