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作者：Fraczek, Krzysztof; Ulcigrai, Corinna
作者单位：Nicolaus Copernicus University; University of Bristol
摘要：We give a criterion which proves non-ergodicity for certain infinite periodic billiards and directional flows on -periodic translation surfaces. Our criterion applies in particular to a billiard in an infinite band with periodically spaced vertical barriers and to the Ehrenfest wind-tree model, which is a planar billiard with a -periodic array of rectangular obstacles. We prove that, in these two examples, both for a full measure set of parameters of the billiard tables and for tables with rat...
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作者：Jossen, Peter
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We show that the statement analogous to the Mumford-Tate conjecture for Abelian varieties holds for 1-motives on unipotent parts. This is done by comparing the unipotent part of the associated Hodge group and the unipotent part of the image of the absolute Galois group with the unipotent part of the motivic fundamental group.
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作者：Bowen, Lewis
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：We determine the range of Furstenberg entropy for stationary ergodic actions of nonabelian free groups by an explicit construction involving random walks on random coset spaces.
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作者：Hairer, M.
作者单位：University of Warwick
摘要：We introduce a new notion of regularity structure that provides an algebraic framework allowing to describe functions and/or distributions via a kind of jet or local Taylor expansion around each point. The main novel idea is to replace the classical polynomial model which is suitable for describing smooth functions by arbitrary models that are purpose-built for the problem at hand. In particular, this allows to describe the local behaviour not only of functions but also of large classes of dis...
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作者：Seidel, Paul
摘要：We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by adding quadratic terms) sufficiently often.
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作者：Koropecki, Andres; Tal, Fabio Armando
作者单位：Universidade Federal Fluminense; Universidade de Sao Paulo
摘要：This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane. This includes all homeomorphisms which have a rotation set with nonempty interior. We define two types of points: inessential and essential. The set of inessential points is shown to be a disjoint union of periodic topological disks (...
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作者：Mironov, Andrey E.
作者单位：Russian Academy of Sciences; Sobolev Institute of Mathematics; Lomonosov Moscow State University
摘要：In this paper we study self-adjoint commuting ordinary differential operators of rank two. We find sufficient conditions when an operator of fourth order commuting with an operator of order 4g+2 is self-adjoint. We introduce an equation on potentials V(x),W(x) of the self-adjoint operator and some additional data. With the help of this equation we find the first example of commuting differential operators of rank two corresponding to a spectral curve of higher genus. These operators have polyn...
