Inventiones mathematicae

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• On hyperboundedness and spectrum of Markov operators AI翻译
  作者：Miclo, Laurent
  作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：Consider an ergodic Markov operator M reversible with respect to a probability measure mu on a general measurable space. It is shown that if M is bounded from L-2(mu) to L-p(mu), where p > 2, then it admits a spectral gap. This result answers positively a conjecture raised by Hoegh-Krohn and Simon (J. Funct. Anal. 9:121-80, 1972) in the more restricted semi-group context. The proof is based on isoperimetric considerations and especially on Cheeger inequalities of higher order forweighted finit...
• A Poincare-Birkhoff theorem for tight Reeb flows on S3 AI翻译
  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...
• Multiple correlation sequences and nilsequences AI翻译
  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...
• Operator renewal theory and mixing rates for dynamical systems with infinite measure (vol 189, pg 61, 2012) AI翻译
  作者：Melbourne, Ian; Terhesiu, Dalia
  作者单位：University of Warwick; University of Vienna
• A solution to the pyjama problem AI翻译
  作者：Manners, Freddie
  作者单位：University of Oxford
  摘要：The pyjama stripe is the subset of consisting of a vertical strip of width around every integer -coordinate. The pyjama problem asks whether finitely many rotations of the pyjama stripe around the origin can cover the plane. The purpose of this paper is to answer this question in the affirmative, for all positive . The problem is reduced to a statement closely related to Furstenberg's Theorem from topological dynamics, and is proved by analogy with that result.
• Whitney-Holder continuity of the SRB measure for transversal families of smooth unimodal maps AI翻译
  作者：Baladi, Viviane; Benedicks, Michael; Schnellmann, Daniel
  作者单位：University of Copenhagen; Royal Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We consider families of nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure of , as a function of on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming existence of a transversal CE parameter, we find a positive measure set of CE parameters , and, for each , a set of polynomially recurrent parameters containing as a Lebesgue density point, and constants , , so that, for every -Holder function , In addition, for all , the renormalis...
• Quasicrystals and Poisson's summation formula AI翻译
  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.
• Combining Riesz bases AI翻译
  作者：Kozma, Gady; Nitzan, Shahaf
  作者单位：Weizmann Institute of Science; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent
  摘要：We show that any finite union of intervals supports a Riesz basis of exponentials.
• MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations AI翻译
  作者：Bayer, Arend; Macri, Emanuele
  作者单位：University of Edinburgh; University System of Ohio; Ohio State University
  摘要：We use wall-crossing with respect to Bridgeland stability conditions to systematically study the birational geometry of a moduli space of stable sheaves on a K3 surface : (a) We describe the nef cone, the movable cone, and the effective cone of in terms of the Mukai lattice of . (b) We establish a long-standing conjecture that predicts the existence of a birational Lagrangian fibration on whenever admits an integral divisor class of square zero (with respect to the Beauville-Bogomolov form). T...
• Unramified division algebras do not always contain Azumaya maximal orders AI翻译
  作者：Antieau, Benjamin; Williams, Ben
  作者单位：University of California System; University of California Los Angeles; University of Southern California
  摘要：We show that, in general, over a regular integral noetherian affine scheme X of dimension at least 6, there exist Brauer classes on X for which the associated division algebras over the generic point have no Azumaya maximal orders over X. Despite the algebraic nature of the result, our proof relies on the topology of classifying spaces of algebraic groups.