Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-17T02:56:45.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Homoclinic points and moduli

Published online by Cambridge University Press:  19 September 2008

Rense A. Posthumus
Rense A. Posthumus
Affiliation:
Department of Mathematics, State University of Groningen, PO Box 800, 9700AV Groningen, The Netherlands
Rights & Permissions [Opens in a new window]

Abstract

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.

In this paper we study some conjugacy invariants (moduli) for discrete two dimensional dynamical systems, with a homoclinic tangency. We show that the modulus obtained by Palis in the heteroclinic case also turns up in the case considered here. We also present two new conjugacy invariants.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 2 , June 1989 , pp. 389 - 398
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[1]Hartman, P.. On local homeomorphisms of Euclidean spaces. Bol. Soc. Math. Mexicana 5 (2) (1960), 220–241.Google Scholar
[2]Hirsch, M.Pugh, C. & Shub, M.. Invariant Manifolds. Lect. Notes in Math. 583 (Springer-Verlag, New York, 1977).Google Scholar
[3]de Melo, W.. Moduli of stability of two dimensional diffeomorphisms. Topology 19 (1980), 9–21.Google Scholar
[4]de Melo, W. & van Strien, S. J.. Diffeomorphisms on surfaces with a finite number of moduli. Erg. Th. & Dynam. Sys. 7 (1987), 415–462.CrossRefGoogle Scholar
[5]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms. Publ. I.H.E.S. 57 (1983), 5–72.Google Scholar
[6]Palis, J.. A differentiable invariant of topological conjugacies and moduli of stability. Asterisque 51 (1978), 335–346.Google Scholar
[7]Palis, J. & de Melo, W.. Geometric Theory of Dynamical Systems: An Introduction (Springer-Verlag, New York, 1982).CrossRefGoogle Scholar
[8]Palis, J. & Takens, F.. Hyperbolicity and the creation of homoclinic orbits. Ann. Math. 125 (2) (1987), 337–374.Google Scholar
[9]Smale, S.. Differentiable dynamical systems. Bull. Am. Soc. 73 (1967), 747–817.Google Scholar