Infinite horseshoes and complex dynamics in physical systems

Samuel Zambrano, Miguel A F Sanjuán

Research output: Contribution to journalArticle

Abstract

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
Volume22
Issue number1-3
DOIs
Publication statusPublished - May 1 2015

Fingerprint

Horseshoe
Complex Dynamics
Nonlinear dynamical systems
Nonlinear Dynamical Systems
Billiards
Stretch
Folding
Rectangle
Phase Space
Dynamical systems
Orbits
Fold
Dynamical system
Orbit
Iteration

Keywords

  • Chaotic scattering
  • Horseshoes
  • Open billiard

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

Infinite horseshoes and complex dynamics in physical systems. / Zambrano, Samuel; Sanjuán, Miguel A F.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 22, No. 1-3, 01.05.2015, p. 866-871.

Research output: Contribution to journalArticle

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