108 citations · 374 across the 17 of their papers we have counts for
11 papers · 1 filter
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…
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…
Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
Irmina Walawska, Daniel Wilczak
We propose a general framework for computer-assisted verification of the presence of symmetry breaking, period-tupling and touch-and-go bifurcations of symmetric periodic orbits fo…
Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation
Daniel Wilczak, Piotr Zgliczyński
We propose a method for computation of stable and unstable sets associated to hyperbolic equilibria of nonautonomous ODEs and for computation of specific type of connecting orbits…
Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system
Daniel Wilczak
We propose a general algorithm for computer assisted verification of uniform hyperbolicity for maps which exhibit a robust attractor. The method has been successfully applied to a…
Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum
Daniel Wilczak, Piotr Zgliczynski
We present a topological method for the efficient computer assisted verification of the existence of the homoclinic tangency which unfolds generically in a one-parameter family of…
Period doubling in the Rossler system - a computer assisted proof
Daniel Wilczak, Piotr Zgliczynski
The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of…
Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - Part II
D. Wilczak, P. Zgliczynski
We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show t…
Topological method for symmetric periodic orbits for maps with a reversing symmetry
D. Wilczak, P. Zgliczynski
We present a topological method of obtaining the existence of infinite number of symmetric periodic orbits for systems with reversing symmetry. The method is based on covering rela…
Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof
D. Wilczak, P. Zgliczynski
The restricted circular three-body problem is considered for the following parameter values , - the values for {\em Oterma} comet in the Sun-Jupiter system. W…