Dynamical and topological aspects of Lyapunov graphs

Autor:	Ketty A. de Rezende, Margarida P. Mello, Maria Alice Bertolim
Rok vydání:	2004
Předmět:	Discrete mathematics Lyapunov function Dynamical systems theory Betti number Applied Mathematics Discrete Morse theory Polytope Morse code Flow network Topology law.invention symbols.namesake law symbols Discrete Mathematics and Combinatorics Circle-valued Morse theory Mathematics
Zdroj:	Qualitative Theory of Dynamical Systems. 4:181-203
ISSN:	1662-3592 1575-5460
DOI:	10.1007/bf02970858
Popis:	In this survey we present the interplay between topological dynamical systems theory with network flow theory in order to obtain a continuation result for abstract Lyapunov graphsL(h 0, …, hn, k) in dimensionn with cycle numberk. We also show that an abstract Lyapunov graph satisfies the Poincare-Hopf inequalities if and only if it satisfies the Morse inequalities and the first Betti number γ1 is greater than or equal tok. We define the Morse polytope determined by the Morse inequalities and describe some of its geometrical properties.
Databáze:	OpenAIRE
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