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

Azevedo, AssisAzevedo, DavideBessa, MárioTorres, Maria Joana2023-05-292023-05-292021A. 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, 2021http://hdl.handle.net/10400.2/13879We 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.engThe closing lemma and the planar general density theorem for Sobolev mapsjournal article10.1090/proc/15352