Weak index pairs and the Conley index for discrete multivalued dynamical systems

2015/11/11 by Batko, Bogdan, Mrozek, Marian
#34C35 #Dynamical Systems (math.DS) #FOS: Mathematics #primary 54H20 #secondary 54C60

paper · doi:10.48550/arxiv.1511.03622

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.

Related

• Conley index for multivalued maps on finite topological spaces
• The Morse equation in the Conley index theory for discrete multivalued dynamical systems
• Conley index for random dynamical systems
• On Conley's Fundamental Theorem of Dynamical Systems
• The Conley index for discrete dynamical systems and the mapping torus