Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778487 | Advances in Mathematics | 2017 | 51 Pages |
Abstract
For linear random dynamical systems in a separable Banach space X, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-k, which present a (quasi)-equivalence relation between the measurably co-invariant cone family and the measurably dominated splitting of X. Moreover, such (quasi)-equivalence relation turns out to be an equivalence relation whenever (i) k=1; or (ii) in the frame of the Multiplicative Ergodic Theorem with certain Lyapunov exponent being greater than the negative infinity. For the second case, we thoroughly investigated the relations between the Lyapunov exponents, the co-invariant cone family and the measurably dominated splitting for linear random dynamical systems in X.
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Physical Sciences and Engineering
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Authors
Zeng Lian, Yi Wang,