scholarly journals Existence and Roughness of the Exponential Dichotomy for Skew-Product Semiflow in Banach Spaces

1995 ◽  
Vol 120 (2) ◽  
pp. 429-477 ◽  
Author(s):  
S.N. Chow ◽  
H. Leiva
Keyword(s):  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Skew Product

scholarly journals On Exponential Dichotomy of Variational Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Bogdan Sasu
Keyword(s):  
Difference Equations ◽  
Exponential Dichotomy ◽  
New Method ◽  
Skew Product ◽  
Skew Product Flows

We give very general characterizations for uniform exponential dichotomy of variational difference equations. We propose a new method in the study of exponential dichotomy based on the convergence of some associated series of nonlinear trajectories. The obtained results are applied to difference equations and also to linear skew-product flows.

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

scholarly journals On exponential dichotomy in Banach spaces

1981 ◽  
Vol 23 (2) ◽  
pp. 293-306 ◽  
Author(s):  
Mihail Megan ◽  
Petre Preda
Keyword(s):  
Banach Space ◽  
Control Systems ◽  
Linear Systems ◽  
Banach Spaces ◽  
Exponential Dichotomy ◽  
Linear Control ◽  
Linear Control Systems

In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems. The obtained results are generalizations of well-known results of W.A. Coppel, J.L. Massera and J.J. Schäffer, K.J. Palmer.

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