We prove exponential decay of correlations for a “reasonable” class of multi-dimensional dispersing billiards. The scatterers are required to be C 3 smooth, the horizon is finite, there are no corner points. In addition, we assume subexponential complexity of the singularity set.
Submitted: November 10, 2007. Accepted: May 23, 2008.
Communicated by Viviane Baladi.
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Bálint, P., Tóth, I.P. Exponential Decay of Correlations in Multi-Dimensional Dispersing Billiards. Ann. Henri Poincaré 9, 1309–1369 (2008). https://doi.org/10.1007/s00023-008-0389-1
- Unstable Manifold
- Riemannian Structure
- Distortion Bound
- Global Constant
- Uniform Hyperbolicity