FoCM 2014 conference

Workshop A1 - Computational Dynamics

December 12, 17:00 ~ 17:25 - Room B21

## An application of the persistence paradigm to the computation of the Conley index

### Paweł Pilarczyk

### Institute of Science and Technology Austria, Austria - pawel.pilarczyk@ist.ac.at

A new idea for determining the Conley index will be introduced, using an approximate isolating neighborhood and an approximation of a map. The approach is based on the persistence paradigm applied to a sequence of candidates for index pairs, whose relative homology is linked by homomorphisms corresponding to inclusions. A construction will be proposed in which the exit set is defined depending on the percentage of the image that falls outside of the neighborhood. A few sample applications of this method to discrete-time dynamical systems and to flows will be shown. These applications are based on combinatorial sets and outer approximations of maps with respect to a cubical grid in the Euclidean space.