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math.DS2025
A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors
Daniel Wilczak, Sergio Serrano, Roberto Barrio
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (disc…
math.DS2025
Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II
Daniel Wilczak, Piotr ZgliczyÅski
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…
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…