Weak index pairs and the Conley index for discrete multivalued dynamical systems
Abstract
Motivated by the problem of reconstructing dynamics from samples we revisit the Conley index theory for discrete multivalued dynamical systems. We introduce a new, less restrictive definition of the isolating neighbourhood. It turns out that then the main tool for the construction of the index, i.e. the index pair, is no longer useful. In order to overcome this obstacle we use the concept of weak index pairs.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.03622
 Bibcode:
 2015arXiv151103622B
 Keywords:

 Mathematics  Dynamical Systems;
 primary 54H20;
 secondary 54C60;
 34C35