Exponential Decay of Correlations in Multi-Dimensional Dispersing Billiards

. 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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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 9; no. 7; pp. 1309 - 1369
Main Authors BALINT, Péter, TOTH, Imre Peter
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.11.2008
Springer
Subjects
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Multivariate analysis
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Probability and statistics
Quantum Field Theory
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Statistics
Theoretical
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Global Constant
Riemannian Structure
Unstable Manifold
Distortion Bound
Uniform Hyperbolicity
Finite horizon
Singularity
Correlation analysis
Correlations
Exponential decay
Mathematical physics
Complexity
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Summary:. 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.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-008-0389-1