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Bibliographic Details
Main Authors: Al-Qaiwani, Rayyan, Callaway, Mark, Rasmussen, Martin
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2412.05603
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author Al-Qaiwani, Rayyan
Callaway, Mark
Rasmussen, Martin
author_facet Al-Qaiwani, Rayyan
Callaway, Mark
Rasmussen, Martin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_05603
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Morse spectrum for linear random dynamical systems
Al-Qaiwani, Rayyan
Callaway, Mark
Rasmussen, Martin
Dynamical Systems
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.
title The Morse spectrum for linear random dynamical systems
topic Dynamical Systems
url https://arxiv.org/abs/2412.05603