The Morse spectrum for linear random dynamical systems
Dynamical Systems
2024-12-10 v1
Abstract
We prove that projectivised finite-dimensional linear random dynamical systems possess a unique finest weak Morse decomposition. Based on this result, we define the Morse spectrum and investigate its basic properties. In particular, we show that the Morse spectrum is given by a finite union of closed intervals. Furthermore we demonstrate that under a bounded growth condition, the Morse spectrum coincides with the non-uniform dichotomy spectrum.
Cite
@article{arxiv.2412.05603,
title = {The Morse spectrum for linear random dynamical systems},
author = {Rayyan Al-Qaiwani and Mark Callaway and Martin Rasmussen},
journal= {arXiv preprint arXiv:2412.05603},
year = {2024}
}