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Session II.1 - Computational Dynamics

Thursday, June 15, 14:30 ~ 15:00

Symbolic dynamics and abundance of connecting orbits between periodic orbits in the Kuramoto-Sivashinsky PDE

Daniel Wilczak

Jagiellonian University, Poland   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

For some parameter value for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we prove the existence of infinite number of homo- and heteroclinic orbits to two periodic orbits. The proof is computer assisted. We present a new algorithm for the rigorous integration of the variational equation (i.e. producing $C^1$ estimates) for a class of dissipative PDEs on the torus.

Joint work with Piotr Zgliczyński (Jagiellonian University, Poland).

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