相关论文: Linearization for difference equations with infini…
We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $\mu$-dichotomy. Under suitable conditions on the nonlinear…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
In this paper we give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible…
The conjugacy problem is one of the central questions in iteration theory. As far as we, for discontinuous strictly monotone maps there is no complete result. In this paper, we investigate the conjugacy problem of strictly monotone maps…
A linear system of difference equations and a nonlinear perturbation are considered. We propose sufficient conditions to ensure that the homeomorphism of topological equivalence between them is actually a $C^1$ diffeomorphism. These…
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 obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed…
In this article we study exponential dichotomies for noninvertible linear difference equations in finite dimensions. After giving the definition, we study the extent to which the projection $P(k)$ in a dichotomy is unique. For equations on…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
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…
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
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…
We consider the conjugate equation driven by two families of finite maps on the unit interval satisfying a compatibility condition. This framework contains de Rham's functional equations. We give sufficient conditions for singularity of the…
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
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,…
An extensive overview of existing criteria, as well as some new uniform exponential stability tests are included for a scalar delay equation $$ \dot{x}(t)+ \sum_{j=1}^n a_j(t)x(h_j(t))=0. $$ Both cases of continuous and measurable…