On Lyapunov exponents of difference equations with random delay

Nguyen Dinh Cong; Thai Son Doan; Stefan Siegmund

doi:10.3934/dcdsb.2015.20.861

Article Contents

2015, Volume 20, Issue 3: 861-874. Doi: 10.3934/dcdsb.2015.20.861

This issue Previous Article Smooth roughness of exponential dichotomies, revisited Next Article The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

On Lyapunov exponents of difference equations with random delay

1.
Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi
2.
Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Ha Noi
3.
Institute for Analysis & Center for Dynamics, Department of Mathematics, Technische Universität Dresden, Zellescher Weg 12-14, 01069 Dresden

Received: October 31, 2013

Revised: July 31, 2014

Published: April 2015

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Abstract

The multiplicative ergodic theorem by Oseledets on Lyapunov spectrum and Oseledets subspaces is extended to linear random difference equations with random delay. In contrast to the general multiplicative ergodic theorem by Lian and Lu, we can prove that a random dynamical system generated by a difference equation with random delay cannot have infinitely many Lyapunov exponents.

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Mathematics Subject Classification: Primary: 37H10, 37H15; Secondary: 39A06.

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