Periodic bounce orbits of prescribed energy

TL;DR

This paper proves the existence of periodic bounce orbits with specified energy levels within bounded domains, providing explicit bounds on their periods and bounce points, advancing understanding of dynamical systems with boundary interactions.

Contribution

It introduces a new proof for the existence of periodic bounce orbits with explicit bounds, a novel result in the study of dynamical systems with boundary conditions.

Findings

Existence of periodic bounce orbits at prescribed energy

Explicit bounds on orbit period

Bounds on the number of bounce points

Abstract

We prove the existence of periodic bounce orbits of prescribed energy on an open bounded domain in Euclidean space. We derive explicit bounds on the period and the number of bounce points.