대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
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  • Pages.243-256
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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HYPERBOLIC STRUCTURE OF POINTWISE INVERSE PSEUDO-ORBIT TRACING PROPERTY FOR C1 DIFFEOMORPHISMS

  • Manseob Lee (Department of Marketing Bog Data and Mathematics Mokwon University)
  • 투고 : 2022.01.14
  • 심사 : 2022.04.22
  • 발행 : 2023.01.31
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초록

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C1 generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

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과제정보

The author would like to thank the reviewers for their useful comments and suggestions.

참고문헌

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