A semi-invertible operator Oseledets theorem
نویسندگان
چکیده
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 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 کاملHölder continuity of Oseledets splittings for semi-invertible operator cocycles
For Hölder continuous cocycles over an invertible, Lipschitz base, we establish the Hölder continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Araújo et al [On Hölder-continuity of Oseledets subspaces J. Lond. Math. Soc. 93 (2016) 194–218] by considering possibly non-invertible cocycles, which, in addition, may take values in the space of com...
متن کاملStochastic Stability of Lyapunov Exponents and Oseledets Splittings for Semi-invertible Matrix Cocycles
We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi-invertible matrix cocycles, subjected to small random perturbations. The first part extends results of Ledrappier and Young [18] to the semiinvertible setting. The second part relies on the study of evolution of subspaces in the Grassmannian, where the analysis developed, based on h...
متن کاملThe Multiplicative Ergodic Theorem of Oseledets
(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.
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2013
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2012.189