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).