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
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