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Continuous-time extensions of discrete-time cocycles

Title data

Chemnitz, Robin ; Engel, Maximilian ; Koltai, Peter:
Continuous-time extensions of discrete-time cocycles.
arXiv , 2023

Official URL: Volltext

Abstract in another language

We consider linear cocycles taking values in $\textup{SL}_d(\mathbb{R})$ driven by homeomorphic transformations of a smooth manifold, in discrete and continuous time. We show that any discrete-time cocycle can be extended to a continuous-time cocycle, while preserving its characteristic properties. We provide a necessary and sufficient condition under which this extension is natural in the sense that the base is extended to an associated suspension flow and that the dimension of the cocycle does not change. Further, we refine our general result for the case of (quasi-)periodic driving. As an example, we present a discrete-time cocycle due to Michael Herman. The Furstenberg--Kesten limits of this cocycle do not exist everywhere and its Oseledets splitting is discontinuous. Our results on the continuous-time extension of discrete-time cocycles allow us to construct a continuous-time cocycle with analogous properties.

Further data

Item Type: Preprint, postprint
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 05 Jul 2023 07:30
Last Modified: 05 Jul 2023 07:30