Nonlinear rotations on a lattice

• Main Authors: Wan Rozali, Wan Nur Fairuz Alwani, Vivaldi, Franco
• Format: Article
• Language: English
• Published: Taylor and Francis 2018
• Subjects: QA300 Analysis
• Online Access: http://irep.iium.edu.my/72019/7/Nonlinear%20rotations%20on%20a%20lattice.pdf; http://irep.iium.edu.my/72019/; https://www.tandfonline.com/doi/abs/10.1080/10236198.2018.1459592?journalCode=gdea20

We consider a prototypical two-parameter family of invertible maps of Z2, 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.