충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제28권2호
  • /
  • Pages.287-305
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  • 2015
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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HYPERBOLICITY FOR CLOSED RELATIONS

  • 투고 : 2015.01.28
  • 심사 : 2015.04.30
  • 발행 : 2015.05.15
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초록

Hyperbolicity is a core of dynamics. Shadowness and expansiveness for homeomorphisms have been studied by J. Om-bach([3], [4], [5]). We study the hyperbolicity (i.e., expansivity and the shadowing property) and the Anosov relation for a closed relation.

키워드

참고문헌

  1. E. Akin, The general Topology of Dynamical Systems, A.M.S, Graduate Studies in Mathematics vol. 1 (1993).
  2. R. McGehee, Attractors for Closed Relations on Compact Hausdorff Spaces, Indiana Univ. Math. J. 41 (1992), 1165-1209. https://doi.org/10.1512/iumj.1992.41.41058
  3. J. Ombach, Equivalent conditions for hyperbolic coordinates, Topology and its App. (1986), 87-90.
  4. J. Ombach, Consequences of the pseudo orbits tracing property and expansiveness, J. Austral. Math. Soc. (1987), 301-313.
  5. J. Ombach, Shadowing, expansivenesss and hyperbolic hoemomorphisms, J. Austral. Math. Soc. (1996), 56-72.
  6. M. Shub and S. Smale, Beyond hyperbolicity, Ann. of Math. 96 (1972), 587-591. https://doi.org/10.2307/1970826
  7. W. Miller and E. Akin, Invariant measures for set-valued dynamical systems, Trans. Amer. Math. Soc. 351 (3), 1203-1225. https://doi.org/10.1090/S0002-9947-99-02424-1