Dimension estimates for nonlinear nonautonomous systems in arbitrary normed spaces

TL;DR

This paper provides explicit dimension estimates for trajectories of nonlinear nonautonomous dynamical systems in arbitrary normed spaces, extending classical results and simplifying growth bounds especially for delay equations.

Contribution

It generalizes Kurzweil's classic results to broader classes of systems and refines dimension estimates for delay equations in normed spaces.

Findings

Derived explicit dimension bounds for nonlinear systems

Extended classical results to nonautonomous and compact systems

Simplified growth bounds for delay equations

Abstract

We calculate explicit estimates for the dimension of trajectories satisfying a certain growth bound. We generalize the classic results of Kurzweil by considering nonlinear nonautonomous and uniformly compact dynamical systems on normed spaces over arbitrary fields. We furthermore refine the results in the case of delay equations, greatly simplifying the relevant growth bounds.