On Unbounded Motions in a Real Analytic Bouncing ball Problem

• Stefano Marò ^[1]
  1. [1] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • 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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