Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T03:30:13.322Z Has data issue: false hasContentIssue false
  • English
  • Français

Extended f-orbits are approximated by orbits

Published online by Cambridge University Press:  22 January 2016

Ken Sawada
Ken Sawada*
Affiliation:
Waseda University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f be a Cr-diffeomorphism, r ≦ 1, on a compact differentiable manifold M with dim M ≧ 2. In [9] F. Takens introduced the concept of extended f-orbits and conjectured the following.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 79 , October 1980 , pp. 33 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[ 1 ] Bowen, R., Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lee. Note in Math. 470, Springer.Google Scholar
[ 2 ] Hirsch, M., Palis, J., Pugh, C. and Shub, M., Neighborhood of hyperbolic sets, Invention Math. 9 (1970), 121–134.Google Scholar
[ 3 ] Hirsch, M. and Pugh, C., Stable manifolds and hyperbolic sets, Global analysis, Proc. Sympo. Pure Math. Vol. XIV, 133–165. Amer. Math. Soc, Providence, R. I. (1970).Google Scholar
[ 4 ] Morimoto, A., Stochastically stable diffeomorphisms and Takens’ conjecture, Local dynamical systems: Integral and differential equations. Lecture Notes No. 303 RIMS (1976), Kyoto University, 8–24.Google Scholar
[ 5 ] Newhouse, S. and Palis, J., Cycles and bifurcation theory, Asterisque 31 (1976), 44–140.Google Scholar
[ 6 ] Nitecki, Z. and Shub, M., Filtrations, decompositions, and explosions, Amer. J. Math. 97 (1976), 1029–1047.CrossRefGoogle Scholar
[ 7 ] Smale, S., The Ω-stability theorem, Global analysis, Proc. Sympo. Pure Math. Vol. XIV, 289–309. Amer. Math. Soc, Providence, R.I. (1970).Google Scholar
[ 8 ] Takens, F., Tolerance stability, Dynamical systems-Warwick 1974, Lee. Notes in Math. 468, Springer, 293–304.Google Scholar