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Attracting invariant curves in planar discrete dynamical systems

Published online by Cambridge University Press:  17 April 2009

Francisco Esquembre
Francisco Esquembre
Affiliation:
Departmento de MatematicasUniversidad de MurciaApartado de Correos 402130071 MurciaSpain
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Abstract

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We study the properties of an invariant attracting curve passing through an attracting fixed point of a planar discrete dynamical system. We compare these properties to the corresponding properties of the invariant repelling curve studied in [3] in order to determine the dynamic behaviour of the system near the fixed point.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 2 , April 1995 , pp. 273 - 286
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Aronson, D.G., Chory, M.A., Hall, G.R. and McGehee, R.P., ‘Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer assisted study’, Comm. Math. Phys. 83 (1982), 303–354.CrossRefGoogle Scholar
[2]Esquembre, F., Rotation sets for circle maps and invariant curves in planar transformations, Ph.D. Thesis (Universidad de Murcia, 1991).Google Scholar
[3]Esquembre, F., ‘Repelling invariant curves in planar discrete dynamical systems’, Bull. Austral. Math. Soc. 49 (1994), 469–481.CrossRefGoogle Scholar
[4]Iooss, G., Bifurcation of Maps and Applications (Noth Holland, 1979).Google Scholar