On (h;k) dichotomy of linear discrete-time systems in Banach spaces
Violeta Crai, Mirela Aldescu
TL;DR
This paper introduces a generalized concept of dichotomy with variable growth rates for linear discrete-time systems in Banach spaces, providing characterizations via Lyapunov sequences and illustrating with examples.
Contribution
It presents a new framework for (h;k) dichotomy in Banach spaces, including characterizations and practical examples.
Findings
Characterization of (h;k) dichotomy using Lyapunov sequences
Extension of dichotomy concepts to variable growth rates
Illustrative examples demonstrating the theory
Abstract
The paper considers a general concept of dichotomy with different growth rates for linear discrete-time systems in Banach spaces. Characterizations in terms of Lyapunov type sequences of norms are given. The approach is illustrated by various examples.
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