Results 41 to 50 of about 42,543 (276)
On attractors, spectra and bifurcations of random dynamical systems [PDF]
, 2015 In this thesis a number of related topics in random dynamical systems theory are studied: local attractors and attractor-repeller pairs, the exponential dichotomy spectrum and bifurcation theory.
Callaway, Mark
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DECOMPOSITION OF Cm THROUGH Q-PERIODIC DISCRETE EVOLUTION FAMILY [PDF]
Matrix Science Mathematic, 2019 Let U={U (m,n) : m,n ∈ Z+} n≥m≥0 be the q-periodic discrete evolution family of square size matrices of order m having complex scalars as entries generated by L(C^m-valued, q-periodic sequence of square size matrices (An)n∈Z+ where q≥2 is a natural ...
Akbar Zada, Hafiz Ullah
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Lyapunov theorems for Banach spaces
, 1993 We present a spectral mapping theorem for semigroups on any Banach space $E$. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for $E$-valued functions.
Latushkin, Yuri +1 more
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Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real Line
Journal of Function Spaces and Applications, 2013 This paper considers two trichotomy concepts in the context of abstract evolution operators. The first one extends the notion of exponential trichotomy in the sense of Elaydi-Hajek for differential equations to abstract evolution operators, and it is a ...
Nicolae Lupa, Mihail Megan
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Exact bounds for exponential dichotomy roughness III. Semistrong dichotomy
Journal of Differential Equations, 1991 [For part II see the above review.] Consider the linear system (1) \(x'=A(t)x\) and its perturbation (2) \(x'=[A(t)+B(t)]x\). In an earlier paper [J. Differ. Equations 71, 63-71 (1988; Zbl 0651.34051)] the author obtained exact bounds for exponential dichotomy roughness by suitably restricting the perturbation term \(B(t)\).
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Nonuniform exponential dichotomies and admissibility
Discrete & Continuous Dynamical Systems - A, 2011 In this paper we consider the relation between the notions of exponential stability and admissibility, in the general context of nonuniform exponential behavior. In particular, we show that with respect to certain adapted norms related to the nonuniform behavior, if any $L^p$ space, with $p\in(1,\infty]$, is admissible for a given evolution process ...
Luis Barreira, Claudia Valls
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On exponential dichotomy in Banach spaces [PDF]
Bulletin of the Australian Mathematical Society, 1981 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 ...
Megan, Mihail, Preda, Petre
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Molecular Oncology, EarlyView.Aldehyde dehydrogenase 1A1 (ALDH1A1) is a cancer stem cell marker in several malignancies. We established a novel epithelial cell line from rectal adenocarcinoma with unique overexpression of this enzyme. Genetic attenuation of ALDH1A1 led to increased invasive capacity and metastatic potential, the inhibition of proliferation activity, and ultimately ...
Martina Poturnajova +25 more
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Nonuniform Dichotomy Spectrum and Normal Forms for Nonautonomous Differential Systems [PDF]
, 2014 The aim of this paper is to study the normal forms of nonautonomous differential systems. For doing so, we first investigate the nonuniform dichotomy spectrum of the linear evolution operators that admit a nonuniform exponential dichotomy, where the ...
Zhang, Xiang
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Exact bounds for exponential dichotomy roughness I. Strong dichotomy
Journal of Differential Equations, 1988 The author considers the unperturbed and perturbed equations (1) \(x'=A(t)x\) and (2) \(y'=[A(t)+B(t)]y,\) where \(t\in {\mathbb{R}}_+\) and A and B are \(n\times n\) matrices. It is shown that if (1) has strong dichotomy on \({\mathbb{R}}_+\), then (2) also has a dichotomy and exact estimates on the exponential dichotomy roughness are obtained.
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