On unbounded motions in a real analytic bouncing ball problem
Dynamical Systems
2022-08-29 v1
Abstract
We consider the model of a ball elastically bouncing on a racket moving in the vertical direction according to a given periodic function . The gravity force is acting on the ball. We prove that if the function belongs to a class of trigonometric polynomials of degree then there exists a one dimensional continuum of initial conditions for which the velocity of the ball tends to infinity. Our result improves a previous one by Pustyl'nikov and gives a new upper bound to the applicability of KAM theory to this model.
Cite
@article{arxiv.2207.12737,
title = {On unbounded motions in a real analytic bouncing ball problem},
author = {Stefano Marò},
journal= {arXiv preprint arXiv:2207.12737},
year = {2022}
}