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A geometric path from zero Lyapunov exponents to rotation cocycles

  • JAIRO BOCHI (a1) and ANDRÉS NAVAS (a2)

Abstract

We consider cocycles of isometries on spaces of non-positive curvature  $H$ . We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there are almost invariant sections, that is, sections that move arbitrarily little under the cocycle dynamics. If, in addition, $H$ is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle.

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A geometric path from zero Lyapunov exponents to rotation cocycles

  • JAIRO BOCHI (a1) and ANDRÉS NAVAS (a2)

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