Is every pseudo-orbit of some homeomorphism near an exact orbit of a nearby homeomorphism?
Bernardi, Olga; Florio, Anna; Wiseman, Jim (2022), Is every pseudo-orbit of some homeomorphism near an exact orbit of a nearby homeomorphism?, Bollettino della Unione Matematica Italiana. 10.1007/s40574-022-00334-8
TypeArticle accepté pour publication ou publié
Journal nameBollettino della Unione Matematica Italiana
MetadataShow full item record
Dipartimento di Matematica Pura e Applicata [Padova]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Mathematics, Agnes Scott College
Abstract (EN)We propose a relaxed notion of shadowing. In particular, for a homeomorphism f on a metric space, we ask whether every approximate orbit is near some actual orbit of some nearby system. We distinguish the cases where the nearby homeomorphism is close or arbitrary close to f. We prove the relations between these notions and ordinary shadowing and present various examples. We finally discuss an application, a C^0-closing lemma for chain recurrent points of a homeomorphism on a topological manifold, not necessarily compact. This result leads to a characterization of explosion phenomena for various recurrent sets on such manifolds.
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