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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$C^2$-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.
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  • 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