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作者：Kwapisz, Jaroslaw
作者单位：Montana State University System; Montana State University Bozeman
摘要：We prove that any expanding linear map that is the inflation map in an inflation-substitution process generating a self-affine tiling of is integral algebraic and Perron. This means that is linearly conjugate to a restriction of an integer matrix to a subspace satisfying a maximal growth condition that generalizes the characterization of Perron numbers as numbers that are larger than the moduli of their algebraic conjugates. The case of diagonalizable has been previously resolved by Richard Ke...
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作者：Avila, Artur; Hubert, Pascal; Skripchenko, Alexandra
作者单位：Universite Paris Cite; Aix-Marseille Universite; HSE University (National Research University Higher School of Economics)
摘要：We study chaotic plane sections of some particular family of triply periodic surfaces. The question about possible behavior of such sections was posed by S. P. Novikov. We prove some estimations on the diffusion rate of these sections using the connection between Novikov's problem and systems of isometries-some natural generalization of interval exchange transformations. Using thermodynamical formalism, we construct an invariant measure for systems of isometries of a special class called the R...
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作者：Calvo, J.; Campos, J.; Caselles, V.; Sanchez, O.; Soler, J.
作者单位：Centre de Recerca Matematica (CRM); University of Granada; Pompeu Fabra University
摘要：A non-linear PDE featuring flux limitation effects together with those of the porous media equation (non-linear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and qualitative behavior of some admissible patterns, namely traveling wave solutions, to this singular reaction-diffusion equation. We show the existence and qualitative behavior of different types of traveling waves: classical profiles for wave speeds high en...
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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 ...
