Zobrazeno 1 - 10
of 185
pro vyhledávání: '"Mrozek, Marian"'
We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components, and the cohomology class of the relation on those components.
Externí odkaz:
http://arxiv.org/abs/2405.16243
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 setting of combinatorial and classical dynamical systems. We prove that a M
Externí odkaz:
http://arxiv.org/abs/2312.08013
Autor:
Edelsbrunner, Herbert, Mrozek, Marian
Taking a discrete approach to functions and dynamical systems, this paper integrates the combinatorial gradients in Forman's discrete Morse theory with persistent homology to forge a unified approach to function simplification. The two crucial ingred
Externí odkaz:
http://arxiv.org/abs/2311.14364
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 which satisfies appropriate regularity conditions, we establish the noti
Externí odkaz:
http://arxiv.org/abs/2310.03099
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rap
Externí odkaz:
http://arxiv.org/abs/2303.02549
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 the Szymczak category over the category of finite sets with arbitrary r
Externí odkaz:
http://arxiv.org/abs/2203.08525
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 a method to track an isolated invariant set -- a salient feature of a
Externí odkaz:
http://arxiv.org/abs/2203.05727
Publikováno v:
Communications in Nonlinear Science and Numerical Simulation 108, article 106226 (30 pages), 2022
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 developed to this end. On the other hand, finding closed orbits in discrete co
Externí odkaz:
http://arxiv.org/abs/2108.13978
Multivector fields provide an avenue for studying continuous dynamical systems in a combinatorial framework. There are currently two approaches in the literature which use persistent homology to capture changes in combinatorial dynamical systems. The
Externí odkaz:
http://arxiv.org/abs/2107.02115
Autor:
Mrozek, Marian, Wanner, Thomas
Connection matrices are one of the central tools in Conley's approach to the study of dynamical systems, as they provide information on the existence of connecting orbits in Morse decompositions. They may be considered a generalisation of the boundar
Externí odkaz:
http://arxiv.org/abs/2103.04269