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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$C^2$-perturbations of Hopf's bifurcation points
and homoclinic tangencies


Authors: J. C. Martín and L. Mora
Journal: Proc. Amer. Math. Soc. 128 (2000), 1241-1245
MSC (1991): Primary 58F12, 58F13; Secondary 58F14, 58F15
Published electronically: August 3, 1999
MathSciNet review: 1637404
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Abstract: In this note we show that a diffeomorphism which has a Hopf's bifurcation point, can be $C^2$ perturbed around the bifurcation point in order to get a diffeomorphism which exhibits homoclinic tangencies. In the $C^3$ case this is not possible because of the typical unfolding of a Hopf's bifurcation point.


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Additional Information

J. C. Martín
Affiliation: Departamento de Matemática, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1086–A, Venezuela
Email: jmartin@usb.ve

L. Mora
Affiliation: Departamento de Matemática, Instituto Venezolano de Investigaciones Científicas, Apartado Postal 21827, Caracas 1020-A, Venezuela
Email: lmora@cauchy.ivic.ve

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05106-0
PII: S 0002-9939(99)05106-0
Received by editor(s): November 10, 1997
Received by editor(s) in revised form: June 4, 1998
Published electronically: August 3, 1999
Communicated by: Mary Rees
Article copyright: © Copyright 2000 American Mathematical Society