LUSTERNIK–SCHNIRELMANN CATEGORY BASED ON THE DISCRETE CONLEY INDEX THEORY

2018 ◽  
Vol 61 (03) ◽  
pp. 693-704
Author(s):  
KATSUYA YOKOI

AbstractWe study Lusternik–Schnirelmann type categories for isolated invariant sets by the use of the discrete Conley index.

2004 ◽  
Vol 2004 (26) ◽  
pp. 1397-1401 ◽  
Author(s):  
M. R. Razvan

We generalize Conley's fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of a regular index filtration for every Morse decomposition.


1987 ◽  
Vol 7 (1) ◽  
pp. 93-103 ◽  
Author(s):  
Andreas Floer

AbstractA compact and isolated invariant set of a continuous flow possesses a so called Conley index, which is the homotopy type of a pointed compact space. For this index a well known continuation property holds true. Our aim is to prove in this context a continuation theorem for the invariant set itself, using an additional structure. This refinement of Conley's index theory will then be used to prove a global and topological continuation-theorem for normally hyperbolic invariant sets.


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