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

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

2008-06-17

arxiv.org/abs/0806.2713v2

Mathematics

Analysis of PDEs

Scientific paper

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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