A family of stadium-like billiards with parabolic boundaries under scaling analysis

Livorati, Andre L. P. [UNESP]; Loskutov, Alexander [UNESP]; Leonel, Edson Denis [UNESP]

A family of stadium-like billiards with parabolic boundaries under scaling analysis

Data

2011-04-29

Autores

Livorati, Andre L. P.

Loskutov, Alexander

Leonel, Edson Denis

Editor

Iop Publishing Ltd

Tipo

Artigo

Direito de acesso

Acesso restrito

Resumo

Some chaotic properties of a family of stadium-like billiards with parabolic focusing components, which is described by a two-dimensional nonlinear area-preserving map, are studied. Critical values of billiard geometric parameters corresponding to a sudden change of the maximal Lyapunov exponent are found. It is shown that the maximal Lyapunov exponent obtained for chaotic orbits of this family is scaling invariant with respect to the control parameters describing the geometry of the billiard. We also show that this behavior is observed for a generic one-parameter family of mapping with the nonlinearity given by a tangent function.