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L-shadowing for the induced hyperspace homeomorphism
Mayara Antunes, Bernardo Carvalho, Welington Cordeiro
We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing pr…
Continuum-wise hyperbolicity, periodic shadowing, and measures of maximal entropy
Bernardo Carvalho, Piotr Oprocha, Elias Rego
We prove that cw-hyperbolic homeomorphisms with jointly continuous stable/unstable holonomies satisfy the periodic shadowing property and, if they are topologically mixing, the per…
Transitivity of real Anosov diffeomorphisms
Bernardo Carvalho
We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensi…
Stable/unstable continua of cw-expansive flows
Alfonso Artigue, Bernardo Carvalho, Margoth Tacuri
We introduce distinct definitions of local stable/unstable sets for flows without fixed points, namely, kinematic, geometric, and sectionally geometric, and discuss relations betwe…
Shadowing in the hyperspace of continua
Bernardo Carvalho, Udayan Darji
We discuss whether classical examples of dynamical systems satisfying the shadowing property also satisfy the shadowing property for the induced map on the hyperspace of continua,…
Gluing-orbit property, local stable/unstable sets, and induced dynamics on hyperspace
Mayara Antunes, Bernardo Carvalho, Welington Cordeiro +1
We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of th…