Entropy formula and continuity of entropy for piecewise expanding maps
| Autor: | José F. Alves, Antonio Pumariño |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Lebesgue measure Applied Mathematics 010102 general mathematics Tangent Dynamical Systems (math.DS) Absolute continuity 01 natural sciences 010101 applied mathematics 37A05 37A10 37A35 37C75} Piecewise FOS: Mathematics Entropy (information theory) Homoclinic orbit 0101 mathematics Mathematics - Dynamical Systems Boltzmann's entropy formula Mathematical Physics Analysis Mathematics Probability measure |
| DOI: | 10.48550/arxiv.1806.01095 |
| Popis: | We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and, using this entropy formula, in some parametrized families we present sufficient conditions for the continuity of that entropy with respect to the parameter. We apply our results to a classical one-dimensional family of tent maps and a family of two-dimensional maps which arises as the limit of return maps when a homoclinic tangency is unfolded by a family of three dimensional diffeomorphisms. Comment: 21 pages, 3 figures |
| Databáze: | OpenAIRE |
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