## Lyapunov Exponents of Linear Cocycles: Continuity via Large DeviationsThe aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach. |

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### Contents

1 | |

2 Estimates on Grassmann Manifolds | 23 |

3 Abstract Continuity of Lyapunov Exponents | 81 |

4 The Oseledets Filtration and Decomposition | 113 |

5 Large Deviations for Random Cocycles | 161 |

### Other editions - View all

Lyapunov Exponents of Linear Cocycles: Continuity via Large Deviations Pedro Duarte,Silvius Klein No preview available - 2016 |

Lyapunov Exponents of Linear Cocycles: Continuity Via Large Deviations Pedro Duarte,Silvius Klein No preview available - 2015 |

### Common terms and phrases

analytic function apply assume assumption Avalanche Principle Banach Banach algebra base dynamics bounded Chap Consider constant convergence defined Definition denote dist(B Dynamical Systems ergodic theorem Euclidean space expanding direction exterior powers fiber LDT estimates finite scale gap pattern Grassmannian Grº Hence Hölder continuity holds implies inequality integers irreducible large deviation LDT parameters Lemma linear cocycle linear map linear subspaces Lipschitz Lyapunov exponents Markov shift Markov system Mat(m Mat(m,R Math matrices measurable cocycles measurable function metric space modulus of continuity Moreover orthogonal Oseledets decomposition Oseledets filtration Plücker embedding probability measure Proof Proposition prove pu-a.e. x e quasi-periodic cocycles satisfies sequence set of measure singular values space of cocycles space of measurable subharmonic functions subspace uniform fiber-LDT variables