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作者：Dujardin, Romain; Lyubich, Mikhail
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); State University of New York (SUNY) System; Stony Brook University; State University of New York (SUNY) System; Stony Brook University
摘要：We study stability and bifurcations in holomorphic families of polynomial automorphisms of . We say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there. We first show that this defines a meaningful notion of stability, which parallels in many ways the classical notion of -stability in one-dimensional dynamics. Define the bifurcation locus to be the complement of the weak stability locus. In the second part of the paper, we prove that under a...
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作者：Mitkovski, Mishko; Poltoratski, Alexei
作者单位：Clemson University; Texas A&M University System; Texas A&M University College Station
摘要：We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their Fourier transform to a finite interval. We apply our results to prove an extension of a theorem by Eremenko and Novikov on the frequency of oscillations of measures with a spectral gap (high-pass signals) near infinity.
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作者：Gao, Su; Jackson, Steve
作者单位：University of North Texas System; University of North Texas Denton
摘要：An equivalence relation E on a standard Borel space is hyperfinite if E is the increasing union of countably many Borel equivalence relations where all -equivalence classs are finite. In this article we establish the following theorem: if a countable abelian group acts on a standard Borel space in a Borel manner then the orbit equivalence relation is hyperfinite. The proof uses constructions and analysis of Borel marker sets and regions in the space This technique is also applied to a problem ...
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作者：Chang, Huai-Liang; Li, Jun; Li, Wei-Ping
作者单位：Hong Kong University of Science & Technology; Fudan University; Stanford University
摘要：For a Landau-Ginzburg space , we construct Witten's top Chern class as an algebraic cycle using cosection localized virtual cycles in the case where all sectors are narrow, verify all axioms of this class, and derive an explicit formula for it in the free case. We prove that this construction is equivalent to the constructions of Polishchuk-Vaintrob, Chiodo, and Fan-Jarvis-Ruan.
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作者：Kollar, Janos; Nemethi, Andras
作者单位：Princeton University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：The study of formal arcs was initiated by Nash in a 1967 preprint. Arc spaces of smooth varieties have a rather transparent structure but difficult problems arise for arcs passing through singularities. The Nash conjecture on the irreducible components of such arc spaces was proved for surfaces by Fernandez de Bobadilla and Pe Pereira and for toric singularities by Ishii and Kollar, but counter examples were found in higher dimensions by Ishii and Kollar, de Fernex and Johnson and Kollar. Here...
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作者：Losev, Ivan
作者单位：Northeastern University
摘要：The main goal of this paper is to compute two related numerical invariants of a primitive ideal in the universal enveloping algebra of a semisimple Lie algebra. The first one, very classical, is the Goldie rank of an ideal. The second one is the dimension of an irreducible module corresponding to this ideal over an appropriate finite W-algebra. We concentrate on the integral central character case. We prove, modulo a conjecture, that in this case the two are equal. Our conjecture asserts that ...
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作者：Bramham, Barney
作者单位：Ruhr University Bochum
摘要：It is an open question in smooth ergodic theory whether there exists a Hamiltonian disk map with zero topological entropy and (strong) mixing dynamics. Weak mixing has been known since Anosov and Katok first constructed examples in 1970. Currently all known examples with weak mixing are irrational pseudo-rotations with Liouvillean rotation number on the boundary. Our main result however implies that for a dense subset of Liouville numbers (strong) mixing cannot occur. Our approach involves app...
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作者：Cieliebak, Kai; Eliashberg, Yakov
作者单位：University of Augsburg; Stanford University
摘要：We give in this article necessary and sufficient conditions on the topology of a compact domain with smooth boundary in C-n, n >= 3, to be isotopic to a rationally or polynomially convex domain.
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作者：Nonnenmacher, Stephane; Zworski, Maciej
作者单位：Universite Paris Saclay; CEA; Centre National de la Recherche Scientifique (CNRS); University of California System; University of California Berkeley
摘要：We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normally hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow is hyperbolic in directions transversal to it. Flows with this structure include contact Anosov flows, classical flows in molecular dynamics, and null geodesic flows for black holes metrics. The decay of correlations is a consequence of the existence of resonance free s...
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作者：Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K.
作者单位：University of Toronto; Rutgers University System; Rutgers University New Brunswick; Harvard University; University of California System; University of California Irvine
