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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...
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作者：Sabok, Marcin
作者单位：McGill University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
摘要：This paper studies the descriptive set-theoretical complexity of the isomorphism problem for separable C*-algebras. We prove that the isomorphism problem for separable (simple, AI) C*-algebras is complete in the class of orbit equivalence relations. This means that any isomorphism problem arising from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple, separable AI C*-algebras.
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作者：Nemirovski, Stefan; Siegel, Kyler
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Ruhr University Bochum; Stanford University
摘要：We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in . We recall some classical obstructions and prove some deeper ones related to symplectic and contact topology. We explain the close connection to Lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces. Our proof also gives a complete characterization of Lagrangian surfaces with open Whitney umbrellas, answering ...
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作者：Juschenko, Kate; Nekrashevych, Volodymyr; de la Salle, Mikael
作者单位：Northwestern University; Texas A&M University System; Texas A&M University College Station; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We show that the amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class of groups, the amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk's group, Basilica group, group associated to Fibonacci tiling, the topological full groups of Cantor minimal systems, groups acting on roote...
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作者：Boyland, Philip; de Carvalho, Andre; Hall, Toby
作者单位：State University System of Florida; University of Florida; Universidade de Sao Paulo; University of Liverpool
摘要：We construct a family of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation set bifurcations and prevalence. We show that there is a full measure subset of [0, 1], consisting of infinitely many mutually disjoint non-trivial closed intervals, on each of which the rotation set mode lo...
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作者：Georgakopoulos, Agelos
作者单位：University of Warwick
摘要：Answering a question of Benjamini and Schramm (Ann Probab 24(3):1219-1238, 1996), we show that the Poisson boundary of any planar, uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised geometrically as a circle, which arises from a discrete version of Riemann's mapping theorem. This implies a conjecture of Northshield (Potential Anal 2(4):299-314, 1993). Some of our technique apply to the non-planar case and might have further applications. When the graph...
