Rapid Decay of Correlations for Nonuniformly Hyperbolic Flows

By Ian Melbourne. 2006

71 citations recorded by the source corpus.

We show that superpolynomial decay of correlations (rapid mixing) is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which Young proved exponential decay of correlations. The proof combines techniques of Dolgopyat and operator renewal theory. It follows from our results that planar periodic Lorentz flows with finite horizons and flows near homoclinic tangencies are typically rapid mixing.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5c3ab207ea81ff6740ddc9803c34451327b10538

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. David Kelly
2. Ian Melbourne
3. Georg A. Gottwald
4. Zemer Kosloff
5. A. Korepanov
6. Peter K. Friz
7. Charalampos Skokos
8. Alexander I. Bufetov

In Statistical and Nonlinear Physics

1. David Kelly
2. Ian Melbourne
3. Georg A. Gottwald
4. Charalampos Skokos
5. Alexander I. Bufetov
6. E. Rio

Citations in the corpus

• Smooth approximation of stochastic differential equations (2014, background): “The simplest case is where there is sufficiently fast uniform contraction along stable manifolds (exponential as assumed in [2, 32, 33], or polynomial as in [1]).”