scholarly journals Uniform Dichotomy Concepts for Discrete-Time Skew Evolution Cocycles in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2177
Author(s):  
Ariana Găină ◽  
Mihail Megan ◽  
Carmen Florinela Popa
Keyword(s):  
Dynamical Systems ◽  
Banach Spaces ◽  
Discrete Time ◽  
Exponential Dichotomy ◽  
Uniform Dichotomy

In the present paper, we consider the problem of dichotomic behaviors of dynamical systems described by discrete-time skew evolution cocycles in Banach spaces. We study two concepts of uniform dichotomy: uniform exponential dichotomy and uniform polynomial dichotomy. Some characterizations of these notions and connections between these concepts are given.

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 Lower semicontinuity of attractors for non-autonomous dynamical systems

2009 ◽  
Vol 29 (6) ◽  
pp. 1765-1780 ◽  
Author(s):  
ALEXANDRE N. CARVALHO ◽  
JOSÉ A. LANGA ◽  
JAMES C. ROBINSON
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Banach Spaces ◽  
Lower Semicontinuity ◽  
Exponential Dichotomy ◽  
Time Dependent ◽  
Unstable Manifolds ◽  
Autonomous Differential Equations ◽  
Autonomous Dynamical Systems

AbstractThis paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

CHAOTIC DYNAMICS FOR MAPS IN ONE AND TWO DIMENSIONS: A GEOMETRICAL METHOD AND APPLICATIONS TO ECONOMICS

2009 ◽  
Vol 19 (10) ◽  
pp. 3283-3309 ◽  
Author(s):  
ALFREDO MEDIO ◽  
MARINA PIREDDU ◽  
FABIO ZANOLIN
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Chaotic Dynamics ◽  
Economic Models ◽  
Two Dimensions ◽  
Geometrical Method ◽  
Mathematical Ideas ◽  
Definition Of ◽  
Applications To Economics ◽  
Discrete Time Dynamical Systems

This article describes a method — called here "the method of Stretching Along the Paths" (SAP) — to prove the existence of chaotic sets in discrete-time dynamical systems. The method of SAP, although mathematically rigorous, is based on some elementary geometrical considerations and is relatively easy to apply to models arising in applications. The paper provides a description of the basic mathematical ideas behind the method, as well as three applications to economic models. Incidentally, the paper also discusses some questions concerning the definition of chaos and some problems arising from economic models in which the dynamics are defined only implicitly.

Sign in / Sign up

Export Citation Format

Share Document