SRB measures of singular hyperbolic attractors

Dominic Veconi

doi:10.3934/dcds.2022020

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2022, Volume 42, Issue 7: 3415-3430. Doi: 10.3934/dcds.2022020

This issue Previous Article Polynomial ergodic averages for certain countable ring actions Next Article Asymptotics of ODE's flow on the torus through a singleton condition and a perturbation result. Applications

SRB measures of singular hyperbolic attractors

Dominic Veconi

Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA

Received: April 30, 2021

Revised: November 30, 2021

Published: July 2022

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Abstract

It is known that 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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Mathematics Subject Classification: Primary: 37C05, 37C40, 37D05, 37D20, 37D45; Secondary: 37C10, 37C70, 37D35.

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