Holger R Dullin and Arnd Bäcker 2001 Nonlinearity 14 1673 doi:10.1088/0951-7715/14/6/314
About ergodicity in the family of limaçon billiards
Holger R Dullin1 and Arnd Bäcker2
Show affiliationsRecommended by T Prosen
By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limaçon billiards. The statistics of these bifurcation shows that the size of the stable intervals decreases with approximately the same rate as their number increases with the period. In particular, we give numerical evidence that arbitrarily close to the cardioid there are elliptic islands due to orbits created in saddle-node bifurcations. This shows explicitly that if in this one-parameter family of maps ergodicity occurs for more than one parameter, the set of these parameter values has a complicated structure.
- PACS
- MSC
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37Axx Ergodic theory (See also 28Dxx)
37G15 Bifurcations of limit cycles and periodic orbits
37D50 Hyperbolic systems with singularities (billiards, etc.)
- Subjects
- Dates
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Issue 6 (November 2001)
Received 4 April 2001
Published 22 October 2001
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About ergodicity in the family of limaçon billiards
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