Livsic theorem for diffeomorphism cocycles

2017/11/06 by Artur Avila, Alejandro Kocsard, Avila, Artur +3 · 1 citation
Mathematics · Physics and Astronomy · #37H05 #37H15 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.1711.02135

openalex publication_date 2017/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the so called Livšic theorem for cocycles taking values in the group of C^1+β-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global in the space of cocycles and thus extends the previous result of the second author and Potrie [KP16] to higher dimensions.

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• Cohomology of Lipschitz-valued cocycles

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