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作者：Bishop, Christopher J.
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We give a method for constructing transcendental entire functions with good control of both the singular values of f and the geometry of f. Among other applications, we construct a function f with bounded singular set, whose Fatou set contains a wandering domain.
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作者：Dumas, David
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the character variety of a surface-one associated with complex projective structures, and the other associated with a 3-manifold. Using the Morgan-Shalen compactification of the character variety and author's results on holonomy limits of complex projective structures, we show that these subvarieties have only a discrete set of intersections. Along the way, we ...
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作者：Avila, Artur
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study Schrodinger operators with a one-frequency analytic potential, focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials. From the dynamical point of view, the transition signals the emergence of non-uniform hyperbolicity, so the dependence of the Lyapunov exponent with respect to parameters plays a central role in the analysis. Though often ill-behaved by conventional measures, we show that the Lyapunov exponent is in ...
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作者：Hesselholt, Lars
作者单位：Nagoya University; University of Copenhagen
摘要：This paper gives a new and direct construction of the multi-prime big de Rham-Witt complex, which is defined for every commutative and unital ring; the original construction by Madsen and myself relied on the adjoint functor theorem and accordingly was very indirect. The construction given here also corrects the 2-torsion which was not quite correct in the original version. The new construction is based on the theory of modules and derivations over a lambda-ring which is developed first. The m...
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作者：Enciso, Alberto; Peralta-Salas, Daniel
作者单位：Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT)
摘要：We prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible Euler equation in . More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in , we show that they can be transformed with a C (m) -small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity. The structure of the vortex lines in the tubes is extremely rich, presenting a positive-measure set of invariant tori and...
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作者：Verbitsky, Misha
作者单位：HSE University (National Research University Higher School of Economics); University of Tokyo
摘要：Let M be a compact complex manifold. The corresponding Teichmuller space Teich is the space of all complex structures on M up to the action of the group of isotopies. The mapping class group acts on Teich in a natural way. An ergodic complex structure is a complex structure with a -orbit dense in Teich. Let M be a complex torus of complex dimension or a hyperkahler manifold with . We prove that M is ergodic, unless M has maximal Picard rank (there are countably many such M). This is used to sh...
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作者：Gorodnik, Alexander; Spatzier, Ralf
作者单位：University of Bristol; University of Bristol; University of Michigan System; University of Michigan
摘要：We study mixing properties of commutative groups of automorphisms acting on compact nilmanifolds. Assuming that every non-trivial element acts ergodically, we prove that such actions are mixing of all orders. We further show exponential 2-mixing and 3-mixing. As an application we prove smooth cocycle rigidity for higher-rank abelian groups of nilmanifold automorphisms.
