1. Lattice Structures for Attractors III
- Author
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Kalies, William D., Mischaikow, Konstantin, and Vandervorst, Robert C. A. M.
- Subjects
Mathematics - Dynamical Systems ,Mathematics - Category Theory ,37B25, 06D05, 37B35 - 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.
- Published
- 2019