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Relations between entropies, exponents and dimensions

Abstract : We focus on the relations between entropies, exponents and dimensions for differentiable dynamics. We propose a simplified proof of Ledrappier-Young entropy formula. Then by using Ledrappier-Young entropy formula and Pesin theory, we bound the entropy of an ergodic measure by a combination of Lyapunov exponents and various invariants on the unstable manifolds such as volume growth, topological entropies and fibered entropies.We also systemically investigate the so called dimensional entropies and their applications to entropy-hyperbolic systems.
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Submitted on : Friday, November 13, 2020 - 3:28:07 PM
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Yuntao Zang. Relations between entropies, exponents and dimensions. Dynamical Systems [math.DS]. Université Paris-Saclay; Soochow university (Suzhou, China), 2020. English. ⟨NNT : 2020UPASS138⟩. ⟨tel-03004242⟩

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