Robust exponential mixing and convergence to equilibrium for singular-hyperbolic attracting sets. (English) Zbl 1530.37052
The authors show the existence of a \(C^2\) open subset \(\mathcal U\) of the space of vector fields such that each vector field \(X \in U\) admits a nontrivial connected singular hyperbolic attracting set \(\Lambda\) such that given \(X \in U\) and \(\mu\) a physical measure supported in \(\Lambda\) the corresponding correlation decays exponentially. They also show exponential convergence to equilibrium.
Reviewer: Miguel Paternain (Montevideo)
MSC:
| 37D05 | Dynamical systems with hyperbolic orbits and sets |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
Keywords:
hyperbolic attracting set; physical measures; SRB measures; robust exponential mixing; exponential convergence to equilibriumReferences:
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