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Quasi-transversal saddle-node bifurcation on surfaces

Published online by Cambridge University Press:  19 September 2008

J. Beloqui  and
M. J. Pacifico
J. Beloqui
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, C.P. 20570, CEP 01498, S. Paulo-SP, Brasil
M. J. Pacifico
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, CEP 21910, Rio de Janeiro-RJ, Brasil
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Abstract

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In this paper we give a complete set of invariants (moduli) for mild and strong semilocal equivalence for certain two parameter families of diffeomorphisms on surfaces. These families exhibit a quasi-transversal saddle-connection between a saddle-node and a hyperbolic periodic point.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 63 - 88
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Beloqui, J.. Modulus of stability for vector fields on 3-manifolds. J. Diff. Equations 65 (1986), 374–395.CrossRefGoogle Scholar
[2]Bogdanov, R.. Deformation verselle d'un point singulier d'un champ de vecteurs sur le plan dans le cas de valeurs propres nulles. Petrovski Seminar 2 (1976).Google Scholar
[3]Bonckaert, P., Dumortier, F. & Van Strien, S.. Singularities in R2 determined by their homogeneous part. To appear.Google Scholar
[4]Chenciner, A.. Bifurcations des points fixes elliptiques. Publ. Math. I.H.E.S. 61 (1985), 67–127.CrossRefGoogle Scholar
[5]de Melo, W.. Moduli of stability of two dimensional diffeomorphisms. Topology 19 (1980), 9–21.CrossRefGoogle Scholar
[6]de Melo, W. & Van Strien, S.. Diffeomorphisms on surfaces with a finite number of moduli. Ergod. Th. & Dynam. Syst. 7 (1987), 415–462.CrossRefGoogle Scholar
[7]Gheiner, J.. On codimension-two bifurcations of diffeomorphisms. Thesis, IMPA.Google Scholar
[8]Palis, J.. A differential invariant of topological conjugacies and moduli of stability. Astérisque 51 (1978), 335–346.Google Scholar
[9]Palis, J. & Smale, S.. Structural Stability Theorems, Global Analysis, vol. XIV, Amer. Math. Soc.: 1970. 223–231.Google Scholar
[10]Newhouse, S. & Palis, J.. Cycles and bifurcation theory. Astérisque 31 (1976), 43–140.Google Scholar
[11]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms. Publ. Math. I.H.E.S. 57 (1983), 5–72.CrossRefGoogle Scholar
[12]Sternberg, S.. On the structure of local homeomorphisms of Euclidean n-space, II. Amer. J. of Math. 80 (1958), 623–631.CrossRefGoogle Scholar
[13]Takens, F.. Partially hyperbolic fixed points. Topology 10 (1971), 133–148.CrossRefGoogle Scholar
[14]Takens, F.. Forced oscillations and bifurcations. Commun. Math. Institute, Rijksuniversiteit Utrecht (1974).Google Scholar
[15]Van Strien, S. J.. One parameter families of vector fields, bifurcations near saddle-connections. (1982) Thesis, Utrecht.Google Scholar