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Annales Henri Poincaré

, Volume 16, Issue 7, pp 1633–1650 | Cite as

Chaotic Dynamics in an Impact Problem

  • Stefano MaròEmail author
Article
  • 94 Downloads

Abstract

We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function f. We show that a modification of a method of Angenent based on sub- and super-solutions can be applied in order to detect chaotic dynamics. Using the theory of exact symplectic twist maps of the cylinder one can prove the result under “natural” conditions on the function f.

Keywords

Recurrence Relation Chaotic Dynamics Exponential Dichotomy Impact Time Bernoulli Shift 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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