On Some Characterizations for Uniform Dichotomy of Evolution Operators in Banach Spaces
Mathematics, 2022 The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces.
Rovana Boruga (Toma), Mihail Megan
doaj +4 more sources
Uniform dichotomy and exponential dichotomy of evolution families on the half-line [PDF]
Journal of Mathematical Analysis and Applications, 2006 The author characterizes uniform and exponential dichotomies of evolution equations on half-lines. With a discrete evolution family \(\Phi = \{\Phi(m,n)\}_{(m,n) \in \Delta}\) associate the subspace \(X_1 = \{x \in X : \Phi(\cdot,0)x \in \ell^\infty(\mathbb{N},X)\}\).
Bogdan Sasu
exaly +3 more sources
Uniform exponential dichotomy of stochastic cocycles [PDF]
Stochastic Processes and Their Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diana Stoica, Stoica, Diana
exaly +3 more sources
Exponential dichotomy for evolution families on the real line [PDF]
Abstract and Applied Analysis, 2006 We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(ℝ,X),Lq(ℝ,X)).
Adina Luminiţa Sasu
doaj +3 more sources
Uniform Dichotomy Concepts for Discrete-Time Skew Evolution Cocycles in Banach Spaces
Mathematics, 2021 In the present paper, we consider the problem of dichotomic behaviors of dynamical systems described by discrete-time skew evolution cocycles in Banach spaces.
Ariana Găină +2 more
doaj +3 more sources
Uniform Detectability of Linear Time Varying Systems With Exponential Dichotomy [PDF]
IEEE Control Systems Letters, 2020 Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially.
Martin Steinberger +2 more
exaly +3 more sources
Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows.
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2003 The authors extend some results of the reviewer, \textit{F. Räbiger} and \textit{R. Schnaubelt} in [Integral Equations Oper. Theory 32, No. 3 , 332--353 (1998; Zbl 0977.34056)] to linear skew-product semiflows by establishing a connection between the uniform exponential dichotomy of these flows and uniform admissibility of several function spaces.
Mihail Megan +2 more
exaly +4 more sources
On Uniform Exponential Dichotomy of Evolution Operators [PDF]
Annals of West University of Timisoara - Mathematics, 2012 The present paper presents three distinct concepts of uniform exponential dichotomy for evolution operators in Banach spaces. Characterizations and relationships between them and some illustrative counterexamples are given.
Mihai Gabriel Babuţia +2 more
openaire +1 more source
On uniform dichotomy in mean of stochastic skew-evolution semiflows in Banach spaces
Annals of the West University of Timisoara: Mathematics and Computer Science, 2023 In this paper we consider three concepts of uniform dichotomy in mean for stochastic skew-evolution semiflows: uniform exponential dichotomy in mean, uniform polynomial dichotomy in mean and uniform h- dichotomy in mean.
Fülöp Tímea Melinda Személy
doaj +1 more source
On uniform exponential
Annales mathématiques Blaise Pascal, 1994 The authors study the problem of uniform exponential \(N\)-dichotomy of evolutionary processes in Banach spaces. Generalizations of some well-known results of R. Datko, Z. Zabczyk, S. Rolewicz and A. Ichikawa are obtained. The obtained results are applicable for a large class of nonlinear differential equations described by A. Ichikawa.
Megan, M., Latcu, D. R.
openaire +2 more sources