Geodesic
On almost specification and average shadowing properties
Marcin Kulczycki 1   ; Dominik Kwietniak 1   ; Piotr Oprocha 2
1 Faculty of Mathematics and Computer Science Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
2 AGH University of Science and Technology Faculty of Applied Mathematics Al. A. Mickiewicza 30 30-059 Kraków, Poland and Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
Fundamenta Mathematicae, Tome 224 (2014) no. 3, pp. 241-278 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in chain transitive systems implies shadowing.
DOI : 10.4064/fm224-3-4
Keywords: study relations between almost specification property asymptotic average shadowing property average shadowing property dynamical systems compact metric spaces implications between these properties relate other important notions shadowing transitivity invariant measures etc provide examples showing compactness necessary condition these implications consequence obtain proof limit shadowing chain transitive systems implies shadowing

Marcin Kulczycki  1   ; Dominik Kwietniak  1   ; Piotr Oprocha  2

1 Faculty of Mathematics and Computer Science Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
2 AGH University of Science and Technology Faculty of Applied Mathematics Al. A. Mickiewicza 30 30-059 Kraków, Poland and Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland 
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 shadowing properties
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 shadowing properties
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Marcin Kulczycki; Dominik Kwietniak; Piotr Oprocha. On almost specification and average
 shadowing properties. Fundamenta Mathematicae, Tome 224 (2014) no. 3, pp. 241-278. doi: 10.4064/fm224-3-4

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