English

SRB measures of singular hyperbolic attractors

Dynamical Systems 2021-12-10 v3

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.

Keywords

Cite

@article{arxiv.2104.10773,
  title  = {SRB measures of singular hyperbolic attractors},
  author = {Dominic Veconi},
  journal= {arXiv preprint arXiv:2104.10773},
  year   = {2021}
}
R2 v1 2026-06-24T01:24:50.476Z