Open AccessSRB measures of singular hyperbolic attractors
Author(s) -
Dominic Veconi
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2022020
Subject(s) - ergodic theory , attractor , mathematics , pure mathematics , gravitational singularity , lorenz system , verifiable secret sharing , type (biology) , discrete mathematics , mathematical analysis , computer science , ecology , set (abstract data type) , biology , programming language
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.