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arXiv · 1709.08904

Nonlinear Rotations on a Lattice

Fairuz Alwani·Franco Vivaldi
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Abstract

We consider a prototypical two-parameter family of invertible maps of $\mathbb{Z}^2$, representing rotations with decreasing rotation number. These maps describe the dynamics inside the island chains of a piecewise affine discrete twist map of the torus, in the limit of fine discretisation. We prove that there is a set of full density of points which, depending of the parameter values, are either periodic or escape to infinity. The proof is based on the analysis of an interval-exchange map over the integers, with infinitely many intervals.

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Fairuz Alwani, Franco Vivaldi. 2017-09-26. Nonlinear Rotations on a Lattice. https://arxiv.org/abs/1709.08904

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