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Exponential Decay of Correlations in Multi-Dimensional Dispersing Billiards

Abstract.

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.

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Correspondence to Péter Bálint.

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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

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Keywords

  • Unstable Manifold
  • Riemannian Structure
  • Distortion Bound
  • Global Constant
  • Uniform Hyperbolicity