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作者：Avila, Artur; Damanik, David; Zhang, Zhenghe
作者单位：University of Zurich; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Rice University; University of California System; University of California Riverside
摘要：We consider discrete one-dimensional Schrodinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant Holder continuous function defined on a subshift of finite type with a fully supported ergodic measure admitting a local product structure and a fixed point, then the Lyapunov exponent is positive away from a discrete set of energies. Moreover, for sampling functions i...
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作者：Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
作者单位：Norwegian University of Science & Technology (NTNU)
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作者：Liu, Yi
作者单位：Peking University
摘要：For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.
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作者：Solecki, Slawomir
作者单位：Cornell University
摘要：We show that, for a generic measure preserving transformation T, the closed group generated by T is not isomorphic to the topological group L-0(lambda, T) of all Lebesgue measurable functions from [0, 1] to T (taken with pointwise multiplication and the topology of convergence in measure). This result answers a question of Glasner and Weiss. The main step in the proof consists of showing that Koopman representations of ergodic boolean actions of L-0(lambda, T) possess a non-trivial spectral pr...
