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Electronic Journal of Qualitative Theory of Differential Equations, 2023 We add relevant references about which we learned after the completion of the initial work. We mainly show how the concept of exponential trichotomy can successfully replace the one of exponential dichotomy in some results from the paper in the title.
Adriana Buică
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Strong and weak admissibility of $L^\infty$ spaces
Electronic Journal of Qualitative Theory of Differential Equations, 2017 For a dynamics with continuous time, we consider the notion of a strong exponential dichotomy with respect to a family of norms and we characterize it in terms of the admissibility of bounded solutions.
Luis Barreira, Claudia Valls
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Exponential Dichotomies and Fredholm Operators [PDF]
Proceedings of the American Mathematical Society, 1988 It is shown that if the operator ( L x ) ( t ) = x ˙ ( t ) − A ( t ) x (
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Non-Atkinson perturbations of nonautonomous linear Hamiltonian systems: exponential dichotomy and nonoscillation [PDF]
, 2017 Producción CientíficaWe analyze the presence of exponential dichotomy (ED) and of global existence of Weyl functions $M^\pm$ for one-parametric families of finite-dimensional nonautonomous linear Hamiltonian systems defined along the orbits of a compact ...
Núñez Jiménez, María del Carmen +1 more
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The Exponential-Time Complexity of Counting (Quantum) Graph Homomorphisms [PDF]
, 2019 Many graph parameters can be expressed as homomorphism counts to fixed target graphs; this includes the number of independent sets and the number of k-colorings for any fixed k.
A Göbel +21 more
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On Exponential Trichotomy of Cocycles over Semiflows
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 The paper considers a concept of exponential trichotomy for cocycles over semiflows in Banach spaces and as a particular case the corresponding dichotomy concept.
Biriş Larisa, Retezan Raluca
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On Tractable Exponential Sums [PDF]
, 2010 We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}} $, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate polynomial with ...
A. Bulatov +10 more
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Tempered exponential behavior for a dynamics in upper triangular form
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We consider the problem of whether the existence of a tempered exponential dichotomy for a linear dynamics can be deduced from the same property for the dynamics restricted to each diagonal entry.
Luis Barreira, Claudia Valls
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Exponential Dichotomy of the Two-Dimensional Linear Differential System
Journal of Mathematics, 2022 This paper deals with a class of two-dimensional linear differential systems with periodic coefficients. A sufficient condition for the exponential dichotomy of the linear system is given by the fixed point theorem and variable substitution, and some ...
Ni Hua, Wang Jing, Bai Min
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Lower semicontinuity of attractors for non-autonomous dynamical systems [PDF]
, 2009 This 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
Abreu +9 more
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