A semi-invertible operator Oseledets theorem

By C. Gonz'alez-Tokman, Anthony Quas. Ergodic Theory and Dynamical Systems, 2011

99 citations recorded by the source corpus.

Abstract 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 of piecewise expanding interval maps randomly chosen from a set of cardinality of the continuum. We also give an application of the theorem to random compositions of perturbations of an expanding map in higher dimensions.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/686562e22839d50d1c8bea07d22244fbc7579962

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Citations in the corpus

An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems (2012, background): “The finite-time constructions considered here are to be contrasted with recent timeasymptotic transfer operator constructions [17, 18, 24], where equivariant Oseledets subspaces play the role of singular vectors in the present paper.”
A volume-based approach to the multiplicative ergodic theorem on Banach spaces (2015, background): “ven when the cocycle is not injective, there is still an invariant, measurably-varying distribution of ‘fast’ growing subspaces, as long as the base dynamics are invertible. Quas and Gonza´lez-Tokman [13] also deduced the existence of an invariant distribution of ‘fast’-growing subspaces for cocycle”