2 problems

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Cocycle rigidity of Jacobians along Lyapunov distributions
Jacobian cocycle-rigidity conjecture. Jacobians along the Lyapunov distributions are cohomologous to constants.
Conjectureopencocycle-rigidity dynamical-systems lyapunov-exponentsarXiv posted 2 days ago
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Rigidity of Jacobians along Lyapunov foliations
Jacobian-rigidity conjecture. Jacobians along Lyapunov foliations for $\alpha$ are rigid.
Conjectureopencocycle-rigidity dynamical-systems measure-rigidityarXiv posted 2 days ago

Cocycle rigidity of Jacobians along Lyapunov distributions