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In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
In this paper we consider some concepts of exponential splitting for nonautonomous linear discrete-time systems. These concepts are generalizations of some well-known concepts of (uniform and nonuniform) exponential dichotomies. Connections…
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
The aim of this paper is to propose a new method to construct exponential attractors for infinite dimensional dynamical systems in Banach spaces with explicit fractal dimension. The approach is established by combing the squeezing…
It was recently shown by the authors that a semilinear elliptic equation can be represented as an infinite-dimensional dynamical system in terms of boundary data on a shrinking one-parameter family of domains. The resulting system is…
By considering the nonuniform exponential dichotomy spectrum, we introduce a global asymptotic nonuniform stability conjecture for nonautonomous differential systems, whose restriction to the autonomous case is related to the classical…
We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…
In this paper we present an overview of results for discrete trigonometric and hyperbolic systems. These systems are discrete analogues of trigonometric and hyperbolic linear Hamiltonian systems. We show results which can be viewed as…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].
In this work we study nonuniform exponential dichotomies and existence of pullback and forward attractors for evolution processes associated to nonautonomous differential equations. We define a new concept of nonuniform exponential…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…
We consider the notion of an exponential dichotomy with respect to a family of norms for an evolutionary family in a Banach space, and we characterize it by the admissibility of the pair $(L^p,L^q)$ for $p,q \in [1,\infty]$ with $p\ge q$.…
We investigate singular perturbation problems caused by small delays in the view of pseudo-exponential dichotomy. For a general linear non-autonomous retarded differential equation with small delay, previous works established the existence…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
We study a liaison between the Bohl's exponents and the exponential dichotomy spectrum of a non autonomous linear system of difference equations on the whole line $\mathbb{Z}$. More specifically, We prove that for any initial condition in…