The Multiplicative Ergodic Theorem of Oseledets
ثبت نشده
چکیده
(n) (x) · v). The map F is called a linear cocycle. Fix some norm ·· on R d , and use the same symbol to indicate the induced operator norm.
منابع مشابه
A semi-invertible operator Oseledets theorem
Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition ...
متن کاملA Concise Proof of the Multiplicative Ergodic Theorem on Banach Spaces
We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with
متن کاملA Semi-invertible Oseledets Theorem with Applications to Transfer Operator Cocycles
Oseledets’ celebrated Multiplicative Ergodic Theorem (MET) [V.I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210.] is concerned with the exponential growth rates of vectors under the action of a linear cocycle on Rd. When the linear actions are invertible, the MET guarantees an almost-everywhere poi...
متن کاملProducts of Random Rectangular Matrices
We study the asymptotic behaviour of points under matrix cocyles generated by rectangular matrices. In particular we prove a random Perron-Frobenius and a Multiplicative Ergodic Theorem. We also provide an example where such products of random rectangular matrices arise in the theory of random walks in random environments and where the Multiplicative Ergodic Theorem can be used to investigate r...
متن کاملOn the Integrability Condition in the Multiplicative Ergodic Theorem for Stochastic Diierential Equations
The multiplicative ergodic theorem is valid under an integrability condition on the linearized ow with respect to an invariant measure. We investigate the case were the ow is generated by a stochastic diierential equation and give a criterion in terms of the vector elds and the (generally non-adapted) invariant measure assuring the validity of the integrability condition.
متن کامل