About ergodicity in the family of limacon billiards
arXiv:nlin/0104003 · doi:10.1088/0951-7715/14/6/314
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.
arXiv comment17 pages, 9 figures
References in corpus (6)
- Generic Twistless Bifurcations
- Homoclinic Bifurcations for the Henon Map
- Edge Diffraction, Trace Formulae and the Cardioid Billiard
- Symbolic Dynamics and Periodic Orbits for the Cardioid Billiard
- Geometry of high-lying eigenfunctions in a plane billiard system having mixed type classical dynamics
- Computing periodic orbits using the anti-integrable limit
Cited by in corpus (14)
- Leaking Chaotic Systems
- Correlation functions of scattering matrix elements in microwave cavities with strong absorption
- Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics
- Current and vortex statistics in microwave billiards
- Chaotic dynamics of the elliptical stadium billiard in the full parameter space
- Chaos in the three-site Bose-Hubbard model -- classical vs quantum
- 3D billiards: visualization of regular structures and trapping of chaotic trajectories
- Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
- Syzygies in the two center problem
- Behaviour of boundary functions for quantum billiards
- Impact of cavity geometry on microlaser dynamics
- Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
- Chaos and stability in a two-parameter family of convex billiard tables
- Chaotic properties of the truncated elliptical billiard