Linear Parabolic Maps on the Torus
chao-dyn
2009-10-31 v1 混沌动力学
摘要
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.
引用
@article{arxiv.chao-dyn/9903017,
title = {Linear Parabolic Maps on the Torus},
author = {Karol Zyczkowski and Takashi Nishikawa},
journal= {arXiv preprint arXiv:chao-dyn/9903017},
year = {2009}
}
备注
22 pages in Latex with 9 pictures in .ps (included)