Lattice Structures for Attractors III
Dynamical Systems
2019-11-22 v1 Category Theory
Abstract
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattices the general notion of `set-difference' taking values in a semilattice is introduced, and is called the Conley form. The Conley form is used to build concrete, set-theoretical models of spectral, or Priestley spaces, of bounded, distributive lattices and their finite coarsenings. Such representations build order-theoretic models of dynamical systems, which are used to develop tools for computing global characteristics of a dynamical system.
Cite
@article{arxiv.1911.09382,
title = {Lattice Structures for Attractors III},
author = {William D. Kalies and Konstantin Mischaikow and Robert C. A. M. Vandervorst},
journal= {arXiv preprint arXiv:1911.09382},
year = {2019}
}