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Average chain transitivity and the almost average shadowing property

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In this paper, we introduce and study notions of average chain transitivity, average chain mixing, total average chain transitivity and almost average shadowing property. We also discuss their interrelations.

Abstract

In this paper, we introduce and study notions of average chain transitivity, average chain mixing, total average chain transitivity and almost average shadowing property. We also discuss their interrelations.

참고문헌 (12)

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  4. Y. Dong, "Ergodic properties of systems with asymptotic average shadowing property", J. Math. Anal. Appl, 432(1), pp.53~73 (2015)
  5. R. Gu, "The asymptotic average shadowing property and transitivity", Nonlinear Anal, 67(6), pp.1680~1689 (2007)
  6. M. Kulczycki, "On almost specification and average shad-owing properties", Fund. Math, 224(3), pp.241~278 (2014)
  7. D. Kwietniak, "A note on the average shadowing property for expansive maps", Topology Appl, 159(1), pp.19~27 (2012)
  8. K. Lee, "Various shadowing properties and their equivalence", Discrete Con-tin. Dyn. Syst, 13(2), pp.533~539 (2005)
  9. Y. Niu, "The average-shadowing property and strong ergodicity", J. Math. Anal. Appl, 376(2), pp.528~534 (2011)
  10. S. Y. Pilyugin, "Shadowing in Dynamical Systems", Lecture Notes in Mathematics, 1706 (1999), Springer-Verlag
  11. D. Richeson, "Chain recurrence rates and topological entropy", Topology Appl, 156(2), pp.251~261 (2008)
  12. K. Sakai, "Various shadowing properties for positively expansive maps", Topology Appl, 131(1), pp.15~31 (2003)

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