$C^2$-perturbations of Hopf’s bifurcation points and homoclinic tangencies
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- by J. C. Martín and L. Mora PDF
- Proc. Amer. Math. Soc. 128 (2000), 1241-1245 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1241-1245
- MSC (1991): Primary 58F12, 58F13; Secondary 58F14, 58F15
- DOI: https://doi.org/10.1090/S0002-9939-99-05106-0
- MathSciNet review: 1637404