Related papers: Nonuniform dichotomy spectrum and reducibility for…
A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…
The main purpose of this paper is to formulate new conditions for smooth linearization of nonautonomous systems with discrete and continuous time. Our results assume that the linear part admits a very general form of dichotomy known as…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…
Sequential dichotomies of general delay equations are not uniform, which was proved two decades ago. This however reminds whether the countably infinite many dichotomies of a neutral equation have the sequential uniformity. In this paper,…
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
To have an uniform estimate for the solutions of the scalar curvature equation perturbed by a non linear term, we give some minimal condition on the scalar curvature.
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
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…
Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true''…
In this paper we introduce the notion of a weak uniform Diophantine exponent of a real number and obtain the complete description of the spectrum of its values.
In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its…