Another proof of Burguet's existence theorem for SRB measures of $C^\infty$ surface diffeomorphisms
J\'er\^ome Buzzi, Sylvain Crovisier, Omri Sarig
TL;DR
This paper provides an alternative proof of Burguet's theorem on the existence of SRB measures for smooth surface diffeomorphisms, building on entropy and Lyapunov exponent analysis.
Contribution
It offers a new proof of Burguet's theorem using entropy and Lyapunov exponents, complementing previous methods.
Findings
Confirmed existence of SRB measures for $C^$ surface diffeomorphisms
Extended understanding of physical measures in dynamical systems
Validated analysis techniques based on entropy and Lyapunov exponents
Abstract
Recently, Burguet proved a strong form of Viana's conjecture on physical measures, in the special case of surface diffeomorphisms. We give another proof, based on our analysis of entropy and Lyapunov exponents in [BCS].
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Stochastic processes and statistical mechanics