SRB measures of singular hyperbolic attractors
Dominic Veconi
TL;DR
This paper establishes verifiable conditions under which singular hyperbolic attractors have finitely many ergodic SRB measures, extending understanding of their statistical properties and providing necessary criteria through examples.
Contribution
It introduces sufficient conditions ensuring a finite number of ergodic SRB measures for singular hyperbolic attractors, with examples demonstrating their necessity.
Findings
Conditions guarantee at most finitely many SRB measures
Examples show conditions are necessary
Includes analysis of Lorenz-type systems
Abstract
It is known that nonuniformly hyperbolic maps admitting singularities have at most countably many ergodic Sinai-Ruelle-Bowen (SRB) measures. These maps include the Belykh attractor, the geometric Lorenz attractor, and more general Lorenz-type systems. In this paper, we establish easily verifiable sufficient conditions guaranteeing that the number of ergodic SRB measures is at most finite, and provide examples and nonexamples showing that the conditions are necessary in general.
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