Admissibility and general dichotomies for evolution families

非自治随机动力系统的容许性与广义非一致二分性

Admissibility and generalized nonuniform dichotomies for nonautonomous Random Dynamical Systems

本文通过容许性方法完整刻画了任意Banach空间上非自治随机线性动力系统的广义非一致二分性，并证明了其在小线性扰动下的鲁棒性。

关于非均匀指数分裂在非局部扰动下的可接受性方法研究

Admissibility approach to nonuniform exponential dichotomies roughness with nonlocal perturbations

本文研究非局部扰动下非均匀指数分裂的保持性，通过函数类可接受性概念建立充分条件，确保分裂结果与同质情况一致。

Admissibility and polynomial dichotomies for evolution families

For an arbitrary evolution family, we consider the notion of a polynomial dichotomy with respect to a family of norms and characterize it in terms of the admissibility property, that is, the existence of a unique bounded solution for each bounded perturbation. In particular, by considering a family of Lyapunov norms, we recover the notion of a (strong) nonuniform polynomial dichotomy. As a nontrivial application of the characterization, we establish the robustness of the notion of a strong nonuniform polynomial dichotomy under sufficiently small linear perturbations.

Admissibility and generalized nonuniform dichotomies for discrete dynamics

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 particular cases, we recover several results in the literature concerning nonuniform exponential dichotomies and nonuniform polynomial dichotomies as well as new results for nonuniform dichotomies with logarithmic growth.

Description of tempered exponential dichotomies by admissibility with no Lyapunov norms

Tempered exponential dichotomy formulates the nonuniform hyperbolicity for random dynamical systems. It was described by admissibility of a pair of function classes defined with Lyapunov norms, For MET-systems (systems satisfying the assumptions of multiplicative ergodic theorem (abbreviated as MET)), it can be described by admissibility of a pair without a Lyapunov norm. However, it is not known how to choose a suitable Lyapunov norms before a tempered exponential dichotomy is given, and there are examples of random systems which are not MET-systems but have a tempered exponential dichotomy. …

Admissibility and nonuniform polynomial dichotomies

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. As a nontrivial application, we establish the robustness of the notion of a nonuniform polynomial dichotomy.