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Homoclinic tangencies: moduli and topology of separatrices

Published online by Cambridge University Press:  19 September 2008

Rense A. Posthumus  and
Floris Takens
Rense A. Posthumus
Affiliation:
PO Box 800, 9700 AV Groningen, The Netherlands
Floris Takens
Affiliation:
PO Box 800, 9700 AV Groningen, The Netherlands
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Extract

We consider two-dimensional diffeomorphisms φ: M → M. For a fixed point p, i.e., p ∈ M and φ(p) = p, we say that q is homoclinic to p if p ≠ q and if both limi→+∞φi(q) and limi→−∞φi(q) are equal to p.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 369 - 385
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

[B,1935]Birkhoff, G. D.. Nouvelles recherches sur les systèmes dynamiques. Mem. Pont. Acad. Novi. Lyncaei 1 (1935), 85–216.Google Scholar
[H,1960]Hartman, P.. On local homeomorphisms of Euclidean spaces. Bol. Soc. Mat. Mexicana 5 (1960), 220–241.Google Scholar
[MS,1987]Melo, W. de & van Strien, S. J.. Diffeomorphisms on surfaces with a finite number of moduli. Ergod. Th. and Dynam. Sys. 7 (1987), 415–462.CrossRefGoogle Scholar
[NPT,1983]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of diffeomorphisms. Publ. Math. IHES 57 (1983), 5–71.CrossRefGoogle Scholar
[P,1890]Poincaré, H.. Sur le problème des trois corps et les équations de la dynamique (Mémoir couronné du prix de S.M. le roi Oscar II de Suède). Acta Math. 13 (1890), 1–270.Google Scholar
[P,1978]Palis, J.. A differentiable invariant of topological conjugacies and moduli of stability. Astérisque 51 (1978), 335–346.Google Scholar
[P,1989]Posthumus, R. A.. Homoclinic points and moduli. Ergod. Th. and Dynam. Sys. 9 (1989), 389–398.CrossRefGoogle Scholar
[PT,1987]Palis, J. & Takens, F.. Hyperbolicity and the creation of homoclinic orbits. Ann. Math. 125 (1987), 337–374.CrossRefGoogle Scholar
[PT,1992]Palis, J. & Takens, F.. Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations. Cambridge University Press: Cambridge, to appear.Google Scholar
[S,1958]Sternberg, S.. On the structure of local homeomorphisms of Euclidean n-space, II. Amer. J. Math. 80 (1958), 623–631.CrossRefGoogle Scholar
[S,1967]Smale, S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747–817.CrossRefGoogle Scholar