Conference abstracts

Session B1 - Computational Dynamics

July 14, 17:00 ~ 17:30

Order theory and Conley’s Connection Matrices

Konstantin Mischaikow

Rutgers University, USA   -   mischaik@math.rutgers.edu

Conley’s decomposition theorem indicates that given any compact invariant set the dynamics off of the associated chain recurrent set is gradient-like. Furthermore, the chain recurrent set can by characterized in terms of the set of attractors and their dual repellers. However, in general invariant sets are not computable and their structure is sensitive to variation in parameters.

In this talk I will focus on efforts to develop a computationally robust theory by replacing invariant sets as the primary object of focus with order theoretic objects such as lattices and posets. In particular, I will discuss recent work on lattices of attracting neighborhoods and associated Morse tilings as a representative of the gradient like structure of dynamics, and attempts to develop an efficient computational framework for Conley’s connection matrix to rigorously identify the structure of the gradient like invariant dynamics.

Joint work with Shaun Harker (Rutgers University, USA), William Kalies (Florida Atlantic University, USA), Kelly Spendlove (Rutgers University, USA) and Robert Vandervorst (VU Amsterdam, Netherlands).

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