4 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…
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…
Self-consistent bounds method for dissipative PDEs
Daniel Wilczak, Piotr ZgliczyÅski
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…