分段旋转：非双射映射的极限集

Pub Date : 2022-02-26 DOI:10.1080/14689367.2022.2132917

Nicolas B'edaride, Jean-Franccois Bertazzon, I. Kabor'e

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引用次数: 0

摘要

我们考虑平面的非对射分段旋转。这些地图属于Boshernitzan和Goetz在之前的论文中介绍的一个家族。本文导出了极限集大小的一些上界。这改进了[M]。Boshernitzan和A. Goetz，两参数分段旋转的二分法，遍历理论动力学。系统23(3)(2003)，第759-770页。

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Piecewise rotations: limit set for the non-bijective maps

We consider non-bijective piecewise rotations of the plane. These maps belong to a family introduced in previous papers by Boshernitzan and Goetz. We derive in this paper some upper bounds to the size of the limit set. This improves results of [M. Boshernitzan and A. Goetz, A dichotomy for a two-parameter piecewise rotation, Ergodic Theory Dynam. Syst. 23(3) (2003), pp. 759–770.].

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