On Unbounded Motions in a Real Analytic Bouncing ball Problem

  1. Stefano Marò 1
  1. 1 Universidad de Oviedo

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2022

Volume: 21

Issue: 4

Type: Article

More publications in: Qualitative theory of dynamical systems


We consider the model of a ball elastically bouncing on a racket moving in the vertical direction according to a given periodic function f (t). The gravity force is acting on the ball. We prove that if the function f (t) belongs to a class of trigonometric polynomials of degree 2 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.

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