Journal
NONLINEARITY
Volume 27, Issue 3, Pages 379-433Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/27/3/379
Keywords
transfer operator; piecewise hyperbolic; billards
Categories
Funding
- NSF [DMS-1101572, DMS-1151762]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1101572] Funding Source: National Science Foundation
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We study the statistical properties of a general class of two-dimensional hyperbolic systems with singularities by constructing Banach spaces on which the associated transfer operators are quasi-compact. When the map is mixing, the transfer operator has a spectral gap and many related statistical properties follow, such as exponential decay of correlations, the central limit theorem, the identification of Ruelle resonances, large deviation estimates and an almost-sure invariance principle. To demonstrate the utility of this approach, we give two applications to specific systems: dispersing billiards with corner points and the reduced maps for certain billiards with focusing boundaries.
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