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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Global structural stability of a saddle node bifurcation


Author: Clark Robinson
Journal: Trans. Amer. Math. Soc. 236 (1978), 155-171
MSC: Primary 58F10
DOI: https://doi.org/10.1090/S0002-9947-1978-0467832-8
MathSciNet review: 0467832
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Abstract: S. Newhouse, J. Palis, and F. Takens have recently proved the global structural stability of a one parameter unfolding of a saddle node when the nonwandering set is finite and transversality conditions are satisfied. (The diffeomorphism is Morse-Smale except for the saddle node.) Using their local unfolding of a saddle node and our method of compatible families of unstable disks (instead of the more restrictive method of compatible systems of unstable tubular families), we are able to extend one of their results to the case where the nonwandering set is infinite. We assume that a saddle node is introduced away from the rest of the nonwandering set which is hyperbolic (Axiom A), and that a (strong) transversality condition is satisfied.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0467832-8
Keywords: Structural stability, bifurcation, saddle node
Article copyright: © Copyright 1978 American Mathematical Society