Hadamard's generalization of hyperbolicity, with applications to the hopf bifurcation problem

  • Neil Fenichel
III. Nonlinear Differential Equations
Part of the Lecture Notes in Physics book series (LNP, volume 38)


Unstable Manifold Stable Manifold Cone Condition Floquet Multiplier Hyperbolicity Condition 


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    Fenichel, N., Asymptotic Stability with Rate Conditions, Indiana Univ. Math. J. 23, 12 (1974) 1109–1137.Google Scholar
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    Fenichel, N., The Orbit Structure of the Hopf Bifurcation Problem, J. Diff. Equations, 17 (1975) 1–21.Google Scholar
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    Hadamard, J., Sur l'Iteration et les Solutions Asymptotiques des Equations Differentielles, Bull. de la Soc. Math. de France 29 (1901) 224–228.Google Scholar
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    Hirsch, M. W. and Pugh, C. C., Stable Manifolds and Hyperbolic Sets, Proc. Symposia in Pure Math., Vol. XIV., Amer. Math. Soc., (1970) 133–163.Google Scholar
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    Ruelle, D., and Takens, F., On the Nature of Turbulence, Comm. Math. Phys. 20 (1971) 167–192.Google Scholar
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    Sacker, R., On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations, New York Univ., IMM-NYU 333, October 1964.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Neil Fenichel
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouver

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