A volume-based approach to the multiplicative ergodic theorem on Banach spaces

Alex  Blumenthal

doi:10.3934/dcds.2016.36.2377

Article Contents

2016, Volume 36, Issue 5: 2377-2403. Doi: 10.3934/dcds.2016.36.2377

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A volume-based approach to the multiplicative ergodic theorem on Banach spaces

Alex Blumenthal^1,

1.
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185

Received: June 30, 2014

Revised: August 31, 2015

Published: May 2017

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Abstract

A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the Lyapunov exponents of a Banach space cocycle.

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Mathematics Subject Classification: Primary: 37H15; Secondary: 37L30, 46B07.

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References

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