1. On homeomorphisms with the two-sided limit shadowing property.
- Author
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Carvalho, Bernardo and Kwietniak, Dominik
- Subjects
- *
HOMEOMORPHISMS , *LIMITS (Mathematics) , *SHADOWING theorem (Mathematics) , *DIFFERENTIABLE dynamical systems , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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