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Shape and Morse theory of attractors
Author(s) -
Kapitanski Lev,
Rodnianski Igor
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200002)53:2<218::aid-cpa2>3.0.co;2-w
Subject(s) - attractor , mathematics , morse code , equivalence (formal languages) , metric space , pure mathematics , circle valued morse theory , morse theory , metric (unit) , space (punctuation) , mathematical analysis , computer science , telecommunications , operations management , economics , operating system
We study the shape (in the sense of Borsuk) of attractors of continuous semi‐dynamical systems on general metric spaces. We show, in particular, that the natural inclusion of the global attractor into the state space is a shape equivalence. This and other results of the paper are used to develop an elementary Morse theory of an attractor. © 2000 John Wiley & Sons, Inc.