scholarly journals Algebraic transition matrices in the Conley index theory

1998 ◽  
Vol 350 (3) ◽  
pp. 889-912 ◽  
Author(s):  
Robert Franzosa ◽  
Konstantin Mischaikow
Keyword(s):  
Index Theory ◽  
Conley Index ◽  
Transition Matrices ◽  
Conley Index Theory

scholarly journals Equivalence of topological and singular transition matrices in the Conley index theory.

1995 ◽  
Vol 42 (2) ◽  
pp. 387-414 ◽  
Author(s):  
Christopher K. McCord ◽  
Konstantin Mischaikow
Keyword(s):  
Index Theory ◽  
Conley Index ◽  
Transition Matrices ◽  
Conley Index Theory

COMPUTATION OF CONNECTION MATRICES USING THE SOFTWARE PACKAGE conley

2009 ◽  
Vol 19 (09) ◽  
pp. 3033-3056
Author(s):  
MOHAMED BARAKAT ◽  
STANISLAUS MAIER-PAAPE
Keyword(s):  
Software Package ◽  
Index Theory ◽  
Conley Index ◽  
Bifurcation Parameter ◽  
Transition Matrices ◽  
Hilliard Equation ◽  
Conley Index Theory ◽  
Connection Matrices ◽  
Cahn Hilliard Equation ◽  
Definition Of

In this paper we demonstrate the power of the computer algebra package conley, which enables one to compute connection and transition matrices, two of the main algebraic tools of the CONLEY index theory. In particular, we study the CAHN–HILLIARD equation on the unit square and extend the results obtained in [Maier-Paape et al., 2007] to a bigger range of the bifurcation parameter. Besides providing several explicit computations using conley, the definition of connection matrices is reconsidered, simplified, and presented in a self-contained manner in the language of CONLEY index theory. Furthermore, we introduce so-called energy induced bifurcation intervals, which can be utilized by conley to differential equations with a parameter. These bifurcation intervals are used to automatically path-follow the set of connection matrices at bifurcation points of the underlying set of equilibria.

LUSTERNIK–SCHNIRELMANN CATEGORY BASED ON THE DISCRETE CONLEY INDEX THEORY

2018 ◽  
Vol 61 (03) ◽  
pp. 693-704
Author(s):  
KATSUYA YOKOI
Keyword(s):  
Index Theory ◽  
Conley Index ◽  
Invariant Sets ◽  
Conley Index Theory ◽  
Lusternik Schnirelmann

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

scholarly journals On Conley's fundamental theorem of dynamical systems

2004 ◽  
Vol 2004 (26) ◽  
pp. 1397-1401 ◽  
Author(s):  
M. R. Razvan
Keyword(s):  
Dynamical Systems ◽  
Fundamental Theorem ◽  
Index Theory ◽  
Conley Index ◽  
Morse Decomposition ◽  
Conley Index Theory

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.

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