Physical measures for ash attractors

In this paper we will prove that any asymptotically sectional-hyperbolic attractor associated to a three-dimensional C2 vector field X supports an unique physical measure. Asymptotic sectional-hyperbolicity means that any point outside of the stable manifolds of the singularities has arbitrarily lar...

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Bibliographic Details
Published in:Journal of Differential Equations 2023-09, Vol.367, p.366-381
Main Authors: San Martín, B., Vivas, Kendry J.
Format: Article
Language:English
Subjects:
Asymptotically sectional-hyperbolic
Attractor
Flow
Physical measure
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Summary:In this paper we will prove that any asymptotically sectional-hyperbolic attractor associated to a three-dimensional C2 vector field X supports an unique physical measure. Asymptotic sectional-hyperbolicity means that any point outside of the stable manifolds of the singularities has arbitrarily large hyperbolic times. Besides, we will describe its main properties and we will deduce some dynamical consequences of the existence of this measure.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2023.05.003