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arXiv · 1911.09382

Lattice Structures for Attractors III

William D. Kalies·Konstantin Mischaikow·Robert C. A. M. Vandervorst
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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.

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William D. Kalies, Konstantin Mischaikow, Robert C. A. M. Vandervorst. 2019-11-21. Lattice Structures for Attractors III. https://arxiv.org/abs/1911.09382

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