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ISSN 1088-6850(e) ISSN 0002-9947(p)

Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle

Author(s): Romain Joly; Geneviève Raugel
Journal: Trans. Amer. Math. Soc. 362 (2010), 5189-5211.
MSC (2010): Primary 35B10, 35B30, 35K57, 37D05, 37D15, 37L45; Secondary 35B40
Posted: May 20, 2010
MathSciNet review: 2657677
Retrieve article in: PDF

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Abstract: In this paper, we show that, for scalar reaction-diffusion equations on the circle , the property of hyperbolicity of all equilibria and periodic orbits is generic with respect to the non-linearity. In other words, we prove that in an appropriate functional space of non-linear terms in the equation, the set of functions, for which all equilibria and periodic orbits are hyperbolic, is a countable intersection of open dense sets. The main tools in the proof are the property of the lap number and the Sard-Smale Theorem.

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