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Weak Strictly Persistence Homeomorphisms and Weak Inverse Shadowing Property and Genericity

Bahman Honary|Alireza Zamani Bahabadi
경북대학교 자연과학대학 수학과|2009.09|Kyungpook Mathematical Journal|제49권 제3호|pp. 411-418

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키워드

shadowing propertyinverse shadowing propertypersistence delta-pseudo-orbit
주제분류수학

초록

In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).

Abstract

In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).

참고문헌 (10)

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  2. 최태영, "Weak inverse shadowing and genericity", 대한수학회보, 43(1), pp.43~52 (2006), 대한수학회
  3. Bahman Honary, "Orbital shadowing property", 대한수학회보, 45(4), pp.645~650 (2008), 대한수학회
  4. P. Walters, "On the pseudo orbit tracing property and its relationship to stability, Lecture Notes in Math", pp.231~244 (1978), Springer
  5. R. Corless, "Approximate and real trajectories for generic dynamical systems", J. Math. Anal. Appl, 189, pp.409~423 (1995)
  6. P. Diamond, "Computer robustness of semihypebolic mappings", Random and computational Dynamics, 3, pp.53~70 (1995)
  7. P. Kloeden, "Continuous and inverse shadowing", Func- tional Di erential Equations, 6, pp.137~153 (1999)
  8. K. Lee, "Continuous inverse shadowing and hyperbolicity", Bull. Austral. Math. Soc, 67, pp.15~26 (2003)
  9. P. Diamond, "Bishadowing and hyperbolicity", International Journal of Bifurcations and chaos, 12, pp.1779~1788 (2002)
  10. K. Kuratowski, "Topology2" (1968), AcademicPress-PWN-PolishSciencePublishers

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