Infinite horseshoes and complex dynamics in physical systems

Samuel Zambrano, Miguel A F Sanjuán

Research output: Contribution to journalArticlepeer-review


Horseshoe maps have played an important role in the study of nonlinear dynamical systems. Here we study maps associated to two simple physical systems: a four-hill potential and an open billiard. They turn out to be very different from the standard horseshoe maps: one iteration stretches and folds a square in phase space an infinite number of times before placing it across itself. In this paper we explore in further depth these infinite horseshoe maps. We show that the infinite folding action requires that the maps are not defined in part of the rectangle. Our exploration also shows that infinite horseshoes provide valuable information on the complexity of the system. In particular, they provide a visual way to code the wide variety of complex orbits existing in the dynamical systems considered.

Original languageEnglish
Pages (from-to)866-871
Number of pages6
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number1-3
Publication statusPublished - May 1 2015


  • Chaotic scattering
  • Horseshoes
  • Open billiard

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics


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