# American Institue of Mathematical Sciences

2008, 7(4): 971-985. doi: 10.3934/cpaa.2008.7.971

## On the Lyapunov dimension of cascade systems

 1 Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom

Received  June 2007 Revised  November 2007 Published  April 2008

In this paper we obtain sharp upper estimates on the uniform Lyapunov dimension of a cascade system in terms of the corresponding Lyapunov exponents of their components. The obtained result is applied for estimating the Lyapunov and fractal dimensions of the attractors of nonautonomous dissipative systems generated by PDEs of mathematical physics.
Citation: Sergey Zelik. On the Lyapunov dimension of cascade systems. Communications on Pure & Applied Analysis, 2008, 7 (4) : 971-985. doi: 10.3934/cpaa.2008.7.971
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