108 citations · 374 across the 17 of their papers we have counts for
18 papers
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…
Self-consistent bounds method for dissipative PDEs
Daniel Wilczak, Piotr Zgliczyński
We discuss the method of self-consistent bounds for dissipative PDEs with periodic boundary conditions. We prove convergence theorems for a class of dissipative PDEs, which constit…
Make Interval Bound Propagation great again
Patryk Krukowski, Daniel Wilczak, Jacek Tabor +2
In various scenarios motivated by real life, such as medical data analysis, autonomous driving, and adversarial training, we are interested in robust deep networks. A network is ro…
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…
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…
Recent advances in rigorous computation of Poincaré maps
Tomasz Kapela, Daniel Wilczak, Piotr Zgliczyński
In this article we present recent advances on interval methods for rigorous computation of Poincaré maps. We also discuss the impact of choice of Poincaré section and coordinate sy…