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

Romain Joly; Geneviève Raugel

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arXiv · 0806.2713

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

Romain Joly·Geneviève Raugel

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Abstract

In this paper, we show that, for scalar reaction-diffusion equations on the circle S1, 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 nonlinear 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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Romain Joly, Geneviève Raugel. 2010-05-10. Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle. https://arxiv.org/abs/0806.2713

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