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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2024

ON THE SPECTRAL THEORY OF GROUPS OF AUTOMORPHISMS OF S-ADIC NILMANIFOLDS

Résumé

Let X be an S-adic compact nilmanifold, equipped with its unique translation invariant probability measure µ. We characterize the countable groups Γ of automorphisms of X for which the Koopman representation κ on L 2 (X, µ) has a spectral gap. More specifically, we show that κ does not have a spectral gap if and only if there exists a non-trivial Γ-invariant quotient solenoid (that is, a finite dimensional, connected, compact abelian group) on which Γ acts as a virtually abelian group.
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Dates et versions

hal-03408669 , version 1 (29-10-2021)

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Citer

Bachir Bekka, Yves Guivarc'H. ON THE SPECTRAL THEORY OF GROUPS OF AUTOMORPHISMS OF S-ADIC NILMANIFOLDS. Ergodic Theory and Dynamical Systems, 2024, 44 (3), pp.705-726. ⟨10.1017/etds.2023.39⟩. ⟨hal-03408669⟩
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