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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：Gogolev, Andrey; Ontaneda, Pedro; Hertz, Federico Rodriguez
作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms. Laying aside many surgery constructions of 3-dimensional Anosov flows, these are the first new examples of manifolds which admit partially hyperbolic diffeomorphisms in the past forty years.
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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.
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作者：Poineau, Jerome; Pulita, Andrea
作者单位：Universite de Caen Normandie; Universite de Montpellier
摘要：We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic zero. Relying on work of the second author who investigated its properties on affinoid domains of the affine line, we prove that its slopes give rise to continuous functions that factorise by the retraction through a locally finite subgraph of the curve.
