## The dynamics of rotating waves in scalar reaction diffusion equations.(English)Zbl 0696.35086

Summary: The maximal compact attractor for the reaction diffusion equation (RDE) $$u_ t=u_{xx}+f(u,u_ x)$$ with periodic boundary conditions is studied. It is shown that any $$\omega$$-limit set contains a rotating wave, i.e., a solution of the form U(x-ct). A number of heteroclinic orbits from one rotating wave to another are constructed. Our main tool is the Nickel-Matano-Henry zero number. The heteroclinic orbits are obtained via a shooting argument, which relies on a generalized Borsuk- Ulam theorem.

### MSC:

 35K57 Reaction-diffusion equations 37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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### References:

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