Boundary crisis and suppression of Fermi acceleration in a dissipative two dimensional non-integrable time-dependent billiard

TL;DR

This paper investigates how dissipation via inelastic collisions affects the dynamics of a two-dimensional time-dependent billiard, demonstrating suppression of Fermi acceleration and the occurrence of a boundary crisis in the system.

Contribution

It introduces a detailed analysis of dissipation effects on Fermi acceleration and chaotic attractors in a non-integrable billiard system, revealing boundary crisis phenomena.

Findings

Dissipation suppresses Fermi acceleration.

Inelastic collisions create and modify attractors.

A boundary crisis occurs with slight changes in damping.

Abstract

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time dependent billiards.