78 citations · 176 across the 18 of their papers we have counts for
23 papers
Morse predecomposition of an ivariant set
Michał Lipiński, Konstantin Mischaikow, Marian Mrozek
Motivated by the study of the recurrent orbits in a Morse set of a Morse decomposition, we introduce the concept of Morse predecomposition of an isolated invariant set in the setti…
Conley index for multivalued maps on finite topological spaces
Jonathan Barmak, Marian Mrozek, Thomas Wanner
We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map wh…
Computing Connection Matrices via Persistence-like Reductions
Tamal K. Dey, Michał Lipiński, Marian Mrozek +1
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for…
Tracking Dynamical Features via Continuation and Persistence
Tamal K. Dey, Michał Lipiński, Marian Mrozek +1
Multivector fields and combinatorial dynamical systems have recently become a subject of interest due to their potential for use in computational methods. In this paper, we develop…
The Szymczak Functor on the Category of Finite Sets and Finite Relations
Mateusz Przybylski, Marian Mrozek, Jim Wiseman
The Szymczak functor is a tool used to construct the Conley index for dynamical systems with discrete time. We present an algorithmizable classification of isomorphism classes in t…
Combinatorial vs. classical dynamics: Recurrence
Marian Mrozek, Roman Srzednicki, Justin Thorpe +1
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been develope…