Exponential decay of correlations for nonuniformly hyperbolic flows with a \(C^{1+\alpha}\) stable foliation, including the classical Lorenz attractor. (English) Zbl 1367.37033
Summary: We prove exponential decay of correlations for a class of \(C^{1+\alpha}\) uniformly hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric Lorenz attractors. As a special case, we show that the classical Lorenz attractor is robustly exponentially mixing.
MSC:
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
| 53D25 | Geodesic flows in symplectic geometry and contact geometry |
| 37C10 | Dynamics induced by flows and semiflows |
Software:
RODESReferences:
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