Robust Exponential Mixing and Convergence to Equilibrium for Singular Hyperbolic Attracting Sets

Abstract

We extend results on robust exponential mixing for geometric Lorenz attractors, with a dense orbit and a unique singularity, to singular-hyperbolic attracting sets with any number of (either Lorenz- or non-Lorenz-like) singularities and finitely many ergodic physical/SRB invariant probability measures, whose basins cover a full Lebesgue measure subset of the trapping region of the attracting set. We obtain exponential mixing for any physical probability measure supported in the trapping region and also exponential convergence to equilibrium, for a $C^2$ open subset of vector fields in any $d$-dimensional compact manifold ($d\ge 3$).

arXiv comment56 pages; 6 figures; minor changes proposed by referees; content as accepted for publication in Journal of Dynamics and Differential Equations, 2022

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Cited by in corpus (1)

• Statistical determinism in non-Lipschitz dynamical systems