Positively N-expansive Homeomorphisms and the L-shadowing Property
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We discuss further the dynamics of n-expansive homeomorphisms with the shadowing property, started in Carvalho and Cordeiro (J Differ Equ 261:3734–3755, 2016). The L-shadowing property is defined and the dynamics of n-expansive homeomorphisms with such property is explored. In particular, we prove that positively n-expansive homeomorphisms with the L-shadowing property can only be defined in finite metric spaces.
KeywordsExpansive n-expansive Shadowing Limit shadowing
Mathematics Subject ClassificationPrimary 37B99 Secondary 37D99
Part of this work was developed while the first author was working at UFV-Brazil and the second author was at IMPA being supported by CNPq(Brazil).