Linear Parabolic Maps on the Torus

Details Linear Parabolic Maps on the Torus Linear Parabolic Maps on the Torus

1999-03-12

arxiv.org/abs/chao-dyn/9903017v1

Phys. Lett. A 259 (1999) 377

Nonlinear Sciences

Chaotic Dynamics

22 pages in Latex with 9 pictures in .ps (included)

Scientific paper

10.1016/S0375-9601(99)00465-X

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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