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arXiv · 2412.05603

The Morse spectrum for linear random dynamical systems

Rayyan Al-Qaiwani·Mark Callaway·Martin Rasmussen
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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.

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Rayyan Al-Qaiwani, Mark Callaway, Martin Rasmussen. 2024-12-07. The Morse spectrum for linear random dynamical systems. https://arxiv.org/abs/2412.05603

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