The structure of the space of ergodic measures of transitive partially hyperbolic sets
| Autor: | Katrin Gelfert, Tiane Marcarini, Lorenzo J. Díaz, Michał Rams |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Transitive relation Mathematics::Dynamical Systems 010505 oceanography General Mathematics 010102 general mathematics Structure (category theory) Dynamical Systems (math.DS) Disjoint sets Space (mathematics) 01 natural sciences Measure (mathematics) Nonlinear Sciences::Chaotic Dynamics Core (graph theory) FOS: Mathematics Ergodic theory Homoclinic orbit Mathematics - Dynamical Systems 37D25 28D20 28D99 37D30 37C29 0101 mathematics 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Monatshefte für Mathematik. 190:441-479 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/s00605-019-01325-2 |
| Popis: | We provide examples of transitive partially hyperbolic dynamics (specific but paradigmatic examples of homoclinic classes) which blend different types of hyperbolicity in the one-dimensional center direction. These homoclinic classes have two disjoint parts: an "exposed" piece which is poorly homoclinically related with the rest and a "core" with rich homoclinic relations. There is an associated natural division of the space of ergodic measures which are either supported on the exposed piece or on the core. We describe the topology of these two parts and show that they glue along nonhyperbolic measures. Measures of maximal entropy are discussed in more detail. We present examples where the measure of maximal entropy is nonhyperbolic. We also present examples where the measure of maximal entropy is unique and nonhyperbolic, however in this case the dynamics is nontransitive. |
| Databáze: | OpenAIRE |
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