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作者：Benoist, Yves; de Saxce, Nicolas
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
摘要：We establish the spectral gap property for dense subgroups generated by algebraic elements in any compact simple Lie group, generalizing earlier results of Bourgain and Gamburd for unitary groups.
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作者：Fayad, Bassam; Kanigowski, Adam
作者单位：Sorbonne Universite; Universite Paris Cite; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：Arnold and Kochergin mixing conservative flows on surfaces stand as the main and almost only natural class of mixing transformations for which higher order mixing has not been established, nor disproved. Under suitable arithmetic conditions on their unique rotation vector, of full Lebesgue measure in the first case and of full Hausdorff dimension in the second, we show that these flows are mixing of any order. For this, we show that they display a generalization of the so called Ratner propert...
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作者：Liu, Jinsong; Zhou, Ze
作者单位：Chinese Academy of Sciences; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：The midscribability theorem, which was first proved by O. Schramm, states that: given a smooth strictly convex body and a convex polyhedron , there exists a convex polyhedron combinatorially equivalent to which midscribes . Here the word midscribe means that all its edges are tangent to the boundary surface of . By using the intersection number technique, together with the Teichmuller theory of packings, this paper provides an alternative approach to this theorem. Furthermore, by combining Sch...
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作者：McLean, Mark
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic to the link of A is said to be Milnor fillable by A. If the first Chern class of our link is torsion then we can assign an invariant of our singularity called the minimal discrepancy, which is an important invariant in birational geometr...
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作者：Levin, Genadi; Przytycki, Feliks; Shen, Weixiao
作者单位：Hebrew University of Jerusalem; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; National University of Singapore; Fudan University
摘要：We prove that for any polynomial map with a single critical point its lower Lyapunov exponent at the critical value is negative if and only if the map has an attracting cycle. Similar statement holds for the exponential maps and some other complex dynamical systems. We prove further that for the unicritical polynomials with positive area Julia sets almost every point of the Julia set has zero Lyapunov exponent. Part of this statement generalizes as follows: every point with positive upper Lyap...
