# The Conley index for discrete dynamical systems and the mapping torus

@article{Weilandt2019TheCI, title={The Conley index for discrete dynamical systems and the mapping torus}, author={Frank Weilandt}, journal={Journal of Applied and Computational Topology}, year={2019}, volume={3}, pages={119-138} }

The classical Conley index for flows is defined as a certain homotopy type. In the case of a discrete dynamical system, one usually considers the shift equivalence class of the so-called index map. This equivalence relation is rarely used in other contexts and not well understood in general. Here we propose using a topological invariant of the shift equivalence definition: The homotopy type of the mapping torus of the index map. Using a homotopy type offers new ways for comparing Conley indices…

## 2 Citations

Analysis of the Element's Arrangement Structures in Discrete Numerical Sequences

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- 2020

Paper contains the results of the analysis of the laws of functioning of discrete dynamical systems, as mathematical models of which, using the apparatus of geometric images of automatons, are used…

The Szymczak Functor on the Category of Finite Sets and Finite Relations

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- 2022

Szymczak functor is a tool used to construct Conley index for dynamical systems with discrete time. We present an algorithmizable classification of isomorphism classes in the Szymczak category over…

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