Sensitivity, local stable/unstable sets and shadowing

AbstractIn this paper, we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that always contain a and perfect subset space. As corollary, generalize results in [Artigue et al. Beyond topological hyperbolicity: Lshadowing property, J. Differ. Equ. 268(6) (2020), pp. 3057–3080.] [Carvalho Cordeiro, Positively N-expansive L-shadowing Dyn. 31(2) (2019), 1005–1016.] proving positively countably expansive spaces satisfying either transitivity or can only be countable spaces.Keywords: Sensitivitystable setshadowing2010 Mathematics Subject Classifications: Primary 37D10Secondary 37B99 AcknowledgmentsWe thank Régis Varão for participating our first virtual meetings during preparation Welington Cordeiro discussions about sensitivity, anonymous referees observations improved presentation paper.Disclosure statementNo potential conflict interest was reported by author(s).Additional informationFundingBernardo Carvalho supported Progetto di Eccellenza MatMod@TOV grant number PRIN 2017S35EHN, CAPES Alexander von Humboldt Foundation under project 88881.162174/2017-1, CNPq 405916/2018-3. Mayara Antunes Margoth Tacuri were also FAPEMIG APQ-00036-22.