28 citations · 31 across the 8 of their papers we have counts for
5 papers · 1 filter
Conley-Morse persistence barcode: a homological signature of combinatorial bifurcations
Tamal K. Dey, Michał Lipiński, Manuel Soriano-Trigueros
Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations…
Computing a Connection Matrix and Persistence Efficiently from a Morse Decomposition
Tamal K. Dey, Michał Lipiński, Andrew Haas
Morse decompositions partition the flows in a vector field into equivalent structures. Given such a decomposition, one can define a further summary of its flow structure by what is…
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…
Testing topological conjugacy of time series
Paweł Dłotko, Michał Lipiński, Justyna Signerska-Rynkowska
This paper considers a problem of testing, from a finite sample, a topological conjugacy of two dynamical systems and . More precisely, given $x_1,\ldots, x_n \subse…
Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
Michał Lipiński, Jacek Kubica, Marian Mrozek +1
We generalize and extend the Conley-Morse-Forman theory for combinatorial multivector fields introduced in \cite{Mr2017}. The generalization consists in dropping the restrictive as…