Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

KUPKA-SMALE DIFFERENTIABLE MAPS

  • Lee, Manseob (Department of Mathematics Mokwon University)
  • Received : 2014.11.11
  • Accepted : 2015.01.30
  • Published : 2015.05.15
Download PDF
⟨ Previous Next ⟩

Abstract

We show that if a regular map belongs to the $C^1$-interior of the set of all Kupka-Smale differentiable maps then it satisfis Axiom A and the strong transverality condition.

Keywords

References

  1. N. Aoki, The set of Axiom A diffeomorphisms with no cycles. Bol. Soc. Bras. Math. 23 (1992), 21-65. https://doi.org/10.1007/BF02584810
  2. N. Aoki, K. Moriyasu and N. Sumi, $C^1$-maps having hyperbolic periodic points, Fund. Math. 169 (2001), 1-49. https://doi.org/10.4064/fm169-1-1
  3. S. Hayashi, Diffeomorphisms in $F^1$(M) satisfy Axiom A, Ergodic Thoery & Dynam. Syst. 12 (1992), 233-253.
  4. M. Hirsh, C. Pugh and M. Shub, "Invariant manifolds.", Lecture Notes in Math. 583, Springer Verlag, Berlin, 1977.
  5. R. Mane, Axiom A for endoemorphisms, Lecture Notes in Math. 597, Springer, 1977, 397-388.
  6. J. Palis, On Morse-Smale dynamical systems, Topology 8 (1969), 385-404. https://doi.org/10.1016/0040-9383(69)90024-X
  7. F. Przytycki, On $\Omega$ -stability and structural stability of endomorphisms satisfying Axiom A, ibid. 60 (1977), 61-77. https://doi.org/10.4064/sm-60-1-61-77
  8. C. Robinson, Structural stability of $C^1$-diffeomorphisms, J. Diff. Equat. 22 (1976), 28-73. https://doi.org/10.1016/0022-0396(76)90004-8
  9. M. Shub, Endormorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175-199. https://doi.org/10.2307/2373276