scholarly journals Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear Discrete-Time Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ioan-Lucian Popa ◽  
Mihail Megan ◽  
Traian Ceauşu
Keyword(s):  
Discrete Time ◽  
Lyapunov Functions ◽  
Exponential Dichotomies ◽  
Discrete Time Systems ◽  
Nonuniform Exponential Dichotomies ◽  
Time Systems

The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential dichotomies of nonautonomous and noninvertible discrete-time systems.

NONUNIFORM EXPONENTIAL BEHAVIOUR AND TOPOLOGICAL EQUIVALENCE

2015 ◽  
Vol 58 (2) ◽  
pp. 279-291
Author(s):  
LUIS BARREIRA ◽  
LIVIU HORIA POPESCU ◽  
CLAUDIA VALLS
Keyword(s):  
Asymptotic Behaviour ◽  
Ergodic Theory ◽  
Canonical Form ◽  
Exponential Dichotomy ◽  
Topological Equivalence ◽  
Exponential Dichotomies ◽  
Exponential Behaviour ◽  
Nonuniform Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomy ◽  
Topological Conjugacies

AbstractWe show that any evolution family with a strong nonuniform exponential dichotomy can always be transformed by a topological equivalence to a canonical form that contracts and/or expands the same in all directions. We emphasize that strong nonuniform exponential dichotomies are ubiquitous in the context of ergodic theory. The main novelty of our work is that we are able to control the asymptotic behaviour of the topological conjugacies at the origin and at infinity.

scholarly journals Nonuniform exponential dichotomies and admissibility

2011 ◽  
Vol 30 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Luis Barreira ◽  
◽  
Claudia Valls ◽  
Keyword(s):  
Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomies

Fredholm operators and nonuniform exponential dichotomies

2016 ◽  
Vol 85 ◽  
pp. 120-127
Author(s):  
Luis Barreira ◽  
Davor Dragičević ◽  
Claudia Valls
Keyword(s):  
Fredholm Operators ◽  
Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomies

Nonuniform exponential dichotomies and Fredholm operators for flows

2017 ◽  
Vol 91 (2) ◽  
pp. 301-316 ◽  
Author(s):  
Luis Barreira ◽  
Davor Dragičević ◽  
Claudia Valls
Keyword(s):  
Fredholm Operators ◽  
Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomies
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