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The closing lemma and the planar general density theorem for Sobolev maps
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-02-12 , DOI: 10.1090/proc/15352 Assis Azevedo , Davide Azevedo , Mário Bessa , Maria Joana Torres
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-02-12 , DOI: 10.1090/proc/15352 Assis Azevedo , Davide Azevedo , Mário Bessa , Maria Joana Torres
Abstract:We prove that given a non-wandering point of a Sobolev-
homeomorphism we can create closed trajectories by making arbitrarily small perturbations. As an application, in the planar case, we obtain that generically the closed trajectories are dense in the non-wandering set.
中文翻译：
Sobolev映射的闭合引理和平面一般密度定理
摘要：我们证明，在Sobolev同胚的非徘徊点的情况下，我们可以通过任意设置较小的扰动来创建闭合轨迹。作为一种应用，在平面情况下，我们获得了一般的闭合轨迹在非漂移集中是密集的。
更新日期：2021-04-12
homeomorphism we can create closed trajectories by making arbitrarily small perturbations. As an application, in the planar case, we obtain that generically the closed trajectories are dense in the non-wandering set. 中文翻译：
Sobolev映射的闭合引理和平面一般密度定理
摘要：我们证明，在Sobolev
同胚的非徘徊点的情况下，我们可以通过任意设置较小的扰动来创建闭合轨迹。作为一种应用，在平面情况下，我们获得了一般的闭合轨迹在非漂移集中是密集的。
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