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Generating partitions for two-dimensional hyperbolic maps

A Bäcker-+ and N Chernov++

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Recommended by A Kupiainen

For a class of two-dimensional hyperbolic maps (which includes certain billiard systems) we construct finite generating partitions. Thus, trajectories of the map can be labelled uniquely by doubly infinite symbol sequences, where the symbols correspond to the atoms of the partition. It is shown that the corresponding conditions are fulfilled in the case of the cardioid billiard, the stadium billiard (and other Bunimovich billiards), planar dispersing and semidispersing billiards.


PACS

05.45.Mt Quantum chaos; semiclassical methods

MSC

37D50 Hyperbolic systems with singularities (billiards, etc.)

81Q50 Quantum chaos (See also 37Dxx)

Subjects

Statistical physics and nonlinear systems

Dates

Issue 1 (January 1998)

Received 25 February 1997, in final form 31 October 1997



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