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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Global structural stability of a saddle node bifurcation
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by Clark Robinson PDF
Trans. Amer. Math. Soc. 236 (1978), 155-171 Request permission

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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • 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