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About ergodicity in the family of limaçon billiards
- Source :
- Nonlinearity. 14:1673-1687
- Publication Year :
- 2001
- Publisher :
- IOP Publishing, 2001.
-
Abstract
- By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limacon 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.<br />17 pages, 9 figures
- Subjects :
- Mathematics::Dynamical Systems
Limaçon
Applied Mathematics
Ergodicity
Mathematical analysis
FOS: Physical sciences
General Physics and Astronomy
Statistical and Nonlinear Physics
Saddle-node bifurcation
Nonlinear Sciences - Chaotic Dynamics
Nonlinear Sciences::Chaotic Dynamics
Continuation
Cardioid
Limit (mathematics)
Chaotic Dynamics (nlin.CD)
Dynamical billiards
Mathematical Physics
Bifurcation
Mathematics
Subjects
Details
- ISSN :
- 13616544 and 09517715
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- Nonlinearity
- Accession number :
- edsair.doi.dedup.....3422280c52ff4da44cdf944bb55270f4