A Grobman–Hartman theorem for general nonuniform exponential dichotomies

Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear Discrete-Time Systems

The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential dichotomies of nonautonomous and noninvertible discrete-time systems.

On the Robustness of Exponential Dichotomies

For linear evolution families in Banach spaces, we establish the robustness of a weaker notion of exponential dichotomy. This notion allows the contraction and expansion along the stable and unstable subspaces to be nonuniform and requires nothing from the angles between these subspaces.

Robustness of nonuniform dichotomies with different growth rates

For nonautonomous linear differential equations v′ = A(t)v in a Banach space, we consider general exponential dichotomies that extend the notion of (uniform) exponential dichotomy in various ways. Namely, the new notion allows: stable and unstable behavior with respect to growth rates e for an arbitrary function ρ(t); nonuniform exponential behavior, causing that any stability or conditional st...

Nonuniform Lower Bounds for Exponential Time Classes

Exponential Dichotomies for Dynamic Equations on Measure Chains

In this paper we introduce the notion of an exponential dichotomy for not necessarily invertible linear dynamic equations in Banach spaces within the framework of the “Calculus on Measure Chains.” Particularly this unifies the corresponding theories for difference and differential equations. We apply our approach to obtain results on perturbed systems. 2000 Mathematics Subject Classification. 3...