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作者：Liu, Si-Qi; Ruan, Yongbin; Zhang, Youjin
作者单位：Tsinghua University; University of Michigan System; University of Michigan
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作者：Mann, Kathryn
作者单位：University of California System; University of California Berkeley
摘要：Let denote the fundamental group of a closed surface of genus . We show that every geometric representation of into the group of orientation-preserving homeomorphisms of the circle is rigid, meaning that its deformations form a single semi-conjugacy class. As a consequence, we give a new lower bound on the number of topological components of the space of representations of into . Precisely, for each nontrivial divisor of , there are at least components containing representations with Euler num...
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作者：Gloria, A.; Neukamm, S.; Otto, F.
作者单位：Universite Libre de Bruxelles; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Max Planck Society
摘要：We study quantitatively the effective large-scale behavior of discrete elliptic equations on the lattice with random coefficients. The theory of stochastic homogenization relates the random, stationary, and ergodic field of coefficients with a deterministic matrix of effective coefficients. This is done via the corrector problem, which can be viewed as a highly degenerate elliptic equation on the infinite-dimensional space of admissible coefficient fields. In this contribution we develop new q...
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作者：Hryniewicz, Umberto; Momin, Al; Salomao, Pedro A. S.
作者单位：Universidade Federal do Rio de Janeiro; Universidade de Sao Paulo
摘要：We consider Reeb flows on the tight 3-sphere admitting a pair of closed orbits forming a Hopf link. If the rotation numbers associated to the transverse linearized dynamics at these orbits fail to satisfy a certain resonance condition then there exist infinitely many periodic trajectories distinguished by their linking numbers with the components of the link. This result admits a natural comparison to the Poincar,-Birkhoff theorem on area-preserving annulus homeomorphisms. An analogous theorem...
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作者：Frantzikinakis, Nikos
作者单位：University of Crete
摘要：We study the structure of multiple correlation sequences defined by measure preserving actions of commuting transformations. When the iterates of the transformations are integer polynomials we prove that any such correlation sequence is the sum of a nilsequence and an error term that is small in uniform density; this was previously known only for measure preserving actions of a single transformation. We then use this decomposition result to give convergence criteria for multiple ergodic averag...
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作者：Lev, Nir; Olevskii, Alexander
作者单位：Bar Ilan University; Tel Aviv University
摘要：We characterize the measures on which have both their support and spectrum uniformly discrete. A similar result is obtained in for positive measures.
