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Exponential Decay of Correlations for Finite Horizon Sinai Billiard Flows

Dynamical Systems 2020-02-25 v3 Mathematical Physics math.MP Spectral Theory Chaotic Dynamics

Abstract

We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L_t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions. (Revised after referees' comments.)

Keywords

Cite

@article{arxiv.1506.02836,
  title  = {Exponential Decay of Correlations for Finite Horizon Sinai Billiard Flows},
  author = {Viviane Baladi and Mark Demers and Carlangelo Liverani},
  journal= {arXiv preprint arXiv:1506.02836},
  year   = {2020}
}

Comments

v2: Revised version after referees' comments. (The homogeneity layers do not appear anymore in the def. of the norm.) The text published in Invent. Math. is v2, but has more pages (due to smaller margins in v2). v3: Contains an additional 2-page note correcting flaws found by M. Jezequel (L 3.2) and D. Thomine (L 4.6 and L 7.5)