Results 11 to 20 of about 42,543 (276)
On Roughness of Exponential Dichotomy
Journal of Mathematical Analysis and Applications, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ju, Ning, Wiggins, Stephen
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Exponential dichotomy and dichotomy radius for difference equations
Journal of Mathematical Analysis and Applications, 2008 The paper deals with a difference equation of the form \[ x(n+1) = A(n)x(n), \;n \in \mathbb{Z}, \quad \tag{1} \] where \(\{A(n)\}_{n \in \mathbb{Z}}\) is a sequence of bounded linear operators on a Banach space \(X.\) The author studies the exponential dichotomy of equation (1) in terms of an admissible pair for the corresponding nonhomogeneous ...
Adina Luminita Sasu
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Exponential dichotomy roughness on Banach spaces
Journal of Mathematical Analysis and Applications, 2006 The author proves roughness results for exponential dichotomies of infinite-dimensional linear equations \[ \dot x = A(t)x . \] An exponential dichotomy on \(\mathbb R\) is rough if there exists \(\delta>0\) such that for \(\sup_{t \in \mathbb R} \| B(t)\| < \delta\) the perturbed equation \[ \dot x = [A(t) + B(t)]x \] also admits an exponential ...
Liviu Horia Popescu
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Generalized exponential dichotomy and global linearization
Journal of Mathematical Analysis and Applications, 2006 The nonautonomous version of the Hartman-Grobman theorem was first proved by Palmer and establishes a topological conjugacy between a nonlinear system \[ x' = A(t)x + f(t,x) \] and its linearization \[ x' = A(t)x, \] under the assumption of \(f\) being bounded with small Lipschitz constant and the linear system admitting an exponential dichotomy.
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EXPONENTIAL DICHOTOMY OF DISCRETE TIME LINEAR SYSTEMS WITH MARKOVIAN JUMPS AND INDEPENDENT RANDOM PERTURBATIONS [PDF]
Fiabilitate şi Durabilitate, 2022 This paper discuses exponential dichotomy problems for a class of discrete-time systems affected by both Markovian jumps and independent random perturbations.
Viorica Mariela UNGUREANU +1 more
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Exponential dichotomy of strongly discontinuous semigroups [PDF]
Bulletin of the Australian Mathematical Society, 1984 In this paper we give necessary and sufficient conditions for exponential dichotomy of a general class of strongly continuous semigroups of operators defined on a Banach space. As a particular case we obtain a Datko theorem for exponential stability of a strongly continuous semigroup of class C0 defined on a Banach space.
Preda, P., Megan, M.
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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
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Nonautonomous Exponential Dichotomy [PDF]
Integral Equations and Operator Theory, 2007 In this note we generalize the strongly continuous bisemigroups generated by exponentially dichotomous operators to so-called bievolution families. These families are then related to strongly continuous bisemigroups on certain Banach spaces of continuous and measurable vector-valued functions.
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Pairs of Function Spaces and Exponential Dichotomy on the Real Line
Advances in Difference Equations, 2010 We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if W∈ℋ(ℝ) and V∈𝒯(ℝ)
Adina Luminiţa Sasu
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Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations
Advances in Nonlinear Analysis, 2021 For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. As an application of the spectral theorem, we prove a reducibility result.
Chu Jifeng +4 more
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