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2025-06-04 07:30:55

Attracting measures
Julian Newman, Peter Ashwin
arxiv.org/abs/2506.02136 arxiv.org/pdf/2506.02136

Attracting measures
Under mild assumptions, the SRB measure $μ$ associated to an Axiom A attractor $A$ has the following properties: (i) the empirical measure starting at a typical point near $A$ converges weakly to $μ$; (ii) the pushforward of any Lebesgue-absolutely continuous probability measure supported near $A$ converges weakly to $μ$. In general, a measure with the first property is called a "physical measure", and physical measures are recognised as generally important in their own right. In this paper,…