Lattice Structures for Attractors III
Lattice Structures for Attractors III
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DOI：
10.1007/s10884-021-10056-8
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发表时间：
2021-10-12
影响因子：
1.3
通讯作者：
Vandervorst, R. C. A. M.
中科院分区：
文献类型：
--
作者：
Kalies, W. D.;Mischaikow, K.;Vandervorst, R. C. A. M.
有界分配格理论为描述动力系统中的方向性和渐近性提供了合适的语言。对于有界分配格，引入了在半格中取值的“集差”的一般概念，称为Conley形式。Conley形式用于建立有界分配格及其有限粗化的谱空间或Priestley空间的具体集合论模型。这些表示表示和计算动力系统的序论模型，例如Morse分解和Morse表示，它们可以被认为是动力系统的整体特征。
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-theoretic models of spectral spaces, or Priestley spaces, of bounded, distributive lattices and their finite coarsenings. Such representations formulate and compute order-theoretic models of dynamical systems such as Morse decompositions and Morse representations, which may be regarded as global characteristics of a dynamical system.