Results 31 to 40 of about 42,543 (276)
Some roughness results concerning reducibility for linear difference equations
International Journal of Mathematics and Mathematical Sciences, 1988 In this paper we prove first that the exponential dichotomy of linear difference equations is rough. Moreover we prove that if the coefficient matrix of a linear difference equation is almost periodic, then the Joint property of having an exponential ...
Garyfalos Papaschinopoulos
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Exponential dichotomies of evolution operators in Banach spaces
, 2014 This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces.
B Sasu +26 more
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On the solvability of the Yakubovich linear-quadratic infinite horizon minimization problem [PDF]
, 2019 The Yakubovich Frequency Theorem, in its periodic version and in its general nonautonomous extension, establishes conditions which are equivalent to the global solvability of a minimization problem of infinite horizon type, given by the integral in ...
Fabbri, Roberta +1 more
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Exponential Dichotomies for Almost Periodic Equations [PDF]
Proceedings of the American Mathematical Society, 1987 It is shown that if an almost periodic equation has an exponential dichotomy on a sufficiently long finite interval, then it has one on ( − ∞ , ∞ ) ( - \infty ,\infty ) .
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Holder Shadowing on Finite Intervals [PDF]
, 2013 For any $\theta, \omega > 1/2$ we prove that, if any $d$-pseudotrajectory of length $\sim 1/d^{\omega}$ of a diffeomorphism $f\in C^2$ can be $d^{\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable.
Anosov +5 more
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A CHARACTERIZATION OF GENERALIZED EXPONENTIAL DICHOTOMY
Journal of Applied Analysis & Computation, 2015 Given the linear system \[ x'(t) = A(t)x(t) \tag{1} \] \((x(t)\) a \(n\)-vector, \(A(t)\) a continuous \(n \times n\) matrix) let \(X(t)\) be a fundamental matrix. The system has an \textit{exponential dichotomy} if there exist a projection \(P\) and two positive constants \(K, \alpha\) with \begin{align*} \|X(t)PX^{-1}(s)\| &\le K \exp(-\alpha(t - s))
Wang, Liugen +2 more
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Almost automorphic delayed differential equations and Lasota-Wazewska model
, 2016 Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of ...
Coronel, Aníbal +3 more
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The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor [PDF]
, 2014 The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact intervals. It is then
Doan, Thai Son +2 more
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Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces
Journal of Function Spaces and Applications, 2013 The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces.
Xiao-qiu Song, Tian Yue, Dong-qing Li
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Almost automorphic solutions of discrete delayed neutral system
, 2015 We study almost automorphic solutions of the discrete delayed neutral dynamic system% \[ x(t+1)=A(t)x(t)+\Delta Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))) \] by means of a fixed point theorem due to Krasnoselskii.
Adıvar, Murat, Koyuncuoglu, H. Can
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