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The asymptotic average shadowing property and transitivity. (English) Zbl 1121.37011
Summary: We introduce the notion of the asymptotic average shadowing property (AASP) and investigate the relation between the AASP and transitivity. It is shown that a continuous map on $$X$$ with the AASP is chain transitive and an $$\mathcal L$$-hyperbolic homeomorphism on $$X$$ with the AASP is topologically transitive, where $$X$$ is a compact metric space.

##### MSC:
 37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 39A10 Additive difference equations 37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics
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