Stickiness in mushroom billiards

Eduardo G. Altmann*, Adilson E. Motter, Holger Kantz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


We investigate the dynamical properties of chaotic trajectories in mushroom billiards. These billiards present a well-defined simple border between a single regular region and a single chaotic component. We find that the stickiness of chaotic trajectories near the border of the regular region occurs through an infinite number of marginally unstable periodic orbits. These orbits have zero measure, thus not affecting the ergodicity of the chaotic region. Notwithstanding, they govern the main dynamical properties of the system. In particular, we show that the marginally unstable periodic orbits explain the periodicity and the power-law behavior with exponent γ=2 observed in the distribution of recurrence times.

Original languageEnglish (US)
Article number033105
Issue number3
StatePublished - Sep 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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