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Singularity Theory and Bifurcation Phenomena in Differential Equations

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Topological Nonlinear Analysis II

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 27))

Abstract

The main objective in singularity theory is to characterize within the class of smooth functions f: ℝn → ℝm those functions which are stable under small perturbations, i.e., to find those functions f which have the property that any nearby smooth function f ∈ is diffeomorphically equivalent to f. This reduces to a local problem, and then to the problem of studying the Taylor expansion of f and trying to determine which terms of the expansion guarantee such a diffeomorphic equivalence.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, I-20133, Milan, Italy

    Bernhard Ruf

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  1. Bernhard Ruf
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  1. Department of Mathematics, University of Rome, Tor Vergata, 00133, Rome, Italy

    Michele Matzeu  & Alfonso Vignoli  & 

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Ruf, B. (1997). Singularity Theory and Bifurcation Phenomena in Differential Equations. In: Matzeu, M., Vignoli, A. (eds) Topological Nonlinear Analysis II. Progress in Nonlinear Differential Equations and Their Applications, vol 27. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4126-3_7

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  • DOI: https://doi.org/10.1007/978-1-4612-4126-3_7

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8665-3

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