Linking Combinatorial and Classical Dynamics: Conley Index and Morse Decompositions

被引：6

作者：

Batko, Bogdan ^{[1
]}

Kaczynski, Tomasz ^{[2
]}

Mrozek, Marian ^{[1
]}

Wanner, Thomas ^{[3
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Div Computat Math, Ul St Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Univ Sherbrooke, Dept Math, 2500 Boul Univ, Sherbrooke, PQ J1K 2R1, Canada

[3] George Mason Univ, Dept Math Sci, Fairfax, VA 22030 USA

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2020年 / 20卷 / 05期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Combinatorial vector field; Multivalued dynamical system; Simplicial complex; Discrete Morse theory; Conley theory; Morse decomposition; Conley-Morse graph; Isolated invariant set; Isolating block; WEAK INDEX; EQUATIONS; FIELDS; PAIRS; MAPS;

D O I：

10.1007/s10208-020-09444-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system Fon the geometric realization of the simplicial complex. Moreover,Fmay be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley-Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case.

引用

页码：967 / 1012

页数：46

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