An investigation of escape and scaling properties of a billiard system.

We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice that the survival probability follows an exponential decay with a characteristic power-law tail when the hole is positioned partially or entirely over large stability islands in phase space.

Dynamics, multistability, and crisis analysis of a sine-circle nontwist map.

We propose a one-dimensional dynamical system, the sine-circle nontwist map, that can be considered a local approximation of the standard nontwist map and an extension of the paradigmatic sine-circle map. The map depends on three parameters, exhibiting a simple mathematical form but with a rich dynamical behavior. We identify periodic, quasiperiodic, and chaotic solutions for different parameter sets with the Lyapunov exponent and Slater's theorem.

Mechanism for stickiness suppression during extreme events in Hamiltonian systems.

In this paper we study how hyperbolic and nonhyperbolic regions in the neighborhood of a resonant island perform an important role allowing or forbidding stickiness phenomenon around islands in conservative systems. The vicinity of the island is composed of nonhyperbolic areas that almost prevent the trajectory to visit the island edge. For some specific parameters tiny channels are embedded in the nonhyperbolic area that are associated to hyperbolic fixed points localized in the neighborhood of the islands.