Naslov
Chaotic properties of the truncated elliptical billiards

Autori
Lopac, Vjera ; Šimić, Ana

Izvornik
Communications in Nonlinear Science and Numerical Simulation (1007-5704) 16 (2011), 1; 309-323

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
truncated eliptical billiard; Poincare sections; chaotic fraction

Sažetak
Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs and their dependence on details of the boundary shapes are studied numerically and analytically. For the two-parameter truncated elliptical billiard (TEB) the existence and linear stability of several periodic orbits are investigated in the full ($\gamma$, $\delta$) parameter space. Poincar\' e plots are computed and used for evaluation of the chaotic fraction of the phase space by means of the box-counting method. The limit of the fully chaotic behavior, identified as $\delta=\sqrt{; ; ; ; ; ; 1-\gamma^2}; ; ; ; ; ; $, corresponds to circular arcs. Above this limit, for flattened elliptical arcs, mixed dynamics with numerous stable elliptic islands is present, similarly as in the elliptical stadium billiards (ESB). Below this limit the full chaos extends over the whole region of elongated shapes and the most of the existing orbits are either neutral or unstable. In both regions numerous parabolic orbits are present, many of them identical to orbits within an ellipse. The chaotic region in the parameter space of the truncated elliptical billiards (TEB) seems to be much larger than was supposed previously. This differs remarkably from the behavior of the elliptical stadium billiards (ESB), where the chaotic region was strictly bounded from both sides. In order to examine transition between TEB and ESB, a generalisation to a novel three-parameter family (GTEB) of stadium-like boundary shapes with elliptical arcs is proposed.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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