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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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Quadratic models for generic local $3$-parameter bifurcations on the plane
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by Freddy Dumortier and Peter Fiddelaers PDF
Trans. Amer. Math. Soc. 326 (1991), 101-126 Request permission

Abstract:

The first chapter deals with singularities occurring in quadratic planar vector fields. We make distinction between singularities which as a general system are of finite codimension and singularities which are of infinite codimension in the sense that they are nonisolated, or Hamiltonian, or integrable, or that they have an axis of symmetry after a linear coordinate change or that they can be approximated by centers. In the second chapter we provide quadratic models for all the known versal $k$-parameter unfoldings with $k = 1,2,3$, except for the nilpotent focus which cannot occur as a quadratic system. We finally show that a certain type of elliptic points of codimension $4$ does not have a quadratic versal unfolding.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 326 (1991), 101-126
  • MSC: Primary 58F14; Secondary 58F36
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1049864-0
  • MathSciNet review: 1049864