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Linear parabolic maps on the torus

✍ Scribed by Karol Życzkowski; Takashi Nishikawa

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 803 KB
Volume: 259
Category: Article
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(99)00465-x

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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