Lyapunov Exponents of Linear Cocycles by Pedro Duarte & Silvius Klein

Author:Pedro Duarte & Silvius Klein
Language: eng
Format: epub
Publisher: Atlantis Press, Paris

2.Every observable satisfies a base-LDT estimate: for every there is , , such that for all we have and

(4.11)

3.Every cocycle with finite maximal Lyapunov exponent is uniformly -bounded, where . For simplicity of notations we let .

4.Every cocycle such that satisfies a uniform fiber-LDT estimate: for all there are and , , such that if with and if then and

(4.12)

As before, , where are such that the deviation size functions are non-increasing, while the deviation set measure functions are continuous and strictly decreasing to 0, as , at least like a power and at most like an exponential. The latter constraint is just for convenience, so we can write, whenever needed, . Moreover, it will be convenient in this section to assume a stronger decay at infinity of , which holds in all our applications. Hence we will assume that

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