Linear parabolic maps on the torus

Karol Zyczkowski, Takashi Nishikawa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image of the unit square into the torus. We study the structure of the maximal invariant set, and in a generic case we prove the sensitive dependence on the initial conditions. We study the decay of correlations and the diffusion in the corresponding system on the plane. We also demonstrate how the rationality of the real numbers defining the map influences the dynamical properties of the system.

Original languageEnglish (US)
Pages (from-to)377-386
Number of pages10
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number5
StatePublished - 1999


  • Decay of correlations
  • Diffusion
  • Parabolic maps on the torus
  • Sensitive dependence on initial conditions

ASJC Scopus subject areas

  • General Physics and Astronomy


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