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math.DS2024
Continuation and bifurcations of periodic orbits and symbolic dynamics in the Swift-Hohenberg equation
Jakub Czwórnóg, Daniel Wilczak
Steady states of the Swift--Hohenberg equation are studied. For the associated four--dimensional ODE we prove that on the energy level two smooth branches of even periodic so…
math.DS2024
Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II
Daniel Wilczak, Piotr Zgliczyński
We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary c…