The Pseudo-Orbit Tracing Property and Expansiveness on the Cantor Set

DOI10.2307/2047397zbMath0666.54024OpenAlexW4232435782MaRDI QIDQ3817289

Takashi Shimomura

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2047397

zbMATH Keywords

Cantor setsubshifts of finite typetopology of uniform convergenceexpansive homeomorphismspseudo-orbit tracing propertytopologically transitive homeomorphismtopologically mixing homeomorphism

Mathematics Subject Classification ID

Dynamical systems with hyperbolic behavior (37D99)

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Shifts of finite type as fundamental objects in the theory of shadowing ⋮ Generic dynamics on compact metric spaces ⋮ Topological stability and shadowing of zero-dimensional dynamical systems ⋮ On genericity of shadowing in one dimension

Cites Work

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• Homeomorphisms with the pseudo orbit tracing property of the Cantor set
• Expansive self-homeomorphisms of the cantor set
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms