The closing lemma and the planar general density theorem for Sobolev maps

Azevedo, Assis; Azevedo, Davide; Bessa, Mário; Torres, Maria Joana

http://hdl.handle.net/10400.2/13879

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Abstract(s)

We prove that given a non-wandering point of a Sobolev-(1,p) 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.

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http://hdl.handle.net/10400.2/13879

Citation

A. Azevedo, D. Azevedo, M. Bessa, M. J. Torres, The closing lemma and the planar general density theorem for Sobolev maps, Proc. Amer. Math. Soc. 149, 1687-1696, 2021