-
作者：Vasseur, Alexis F.; Yu, Cheng
作者单位：University of Texas System; University of Texas Austin
摘要：In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins (Commun Math Phys 238:211-223 2003) entropy conservation. The main contribution of this paper is to derive the Mellet and Vasseur (Commun Partial Differ Equ 32:431-452, 2007) type inequality for weak solutions, even if it is not verified by the first level of approximation. This provides existence of global soluti...
-
作者：Damanik, David; Gorodetski, Anton; Yessen, William
作者单位：Rice University; University of California System; University of California Irvine
摘要：We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and establish relations between its spectrum and spectral characteristics (namely, the optimal Holder exponent of the integrated density of states, the dimension of the density of states measure, the dimension of the spectrum, and the upper transport exponent) and the dynamical properties of the Fibonacci trace map (such as dimensional characteristics of the non-wand...
-
作者：Bonatti, Christian; Gogolev, Andrey; Potrie, Rafael
作者单位：Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); State University of New York (SUNY) System; Binghamton University, SUNY; Universidad de la Republica, Uruguay
摘要：We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms f on compact 3-manifolds with fundamental groups of exponential growth such that is not homotopic to identity for all . These provide counterexamples to a classification conjecture of Pujals.
-
作者：Sabok, Marcin
作者单位：McGill University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
摘要：This paper studies the descriptive set-theoretical complexity of the isomorphism problem for separable C*-algebras. We prove that the isomorphism problem for separable (simple, AI) C*-algebras is complete in the class of orbit equivalence relations. This means that any isomorphism problem arising from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple, separable AI C*-algebras.
-
作者：Juschenko, Kate; Nekrashevych, Volodymyr; de la Salle, Mikael
作者单位：Northwestern University; Texas A&M University System; Texas A&M University College Station; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We show that the amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class of groups, the amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk's group, Basilica group, group associated to Fibonacci tiling, the topological full groups of Cantor minimal systems, groups acting on roote...
-
作者：Boyland, Philip; de Carvalho, Andre; Hall, Toby
作者单位：State University System of Florida; University of Florida; Universidade de Sao Paulo; University of Liverpool
摘要：We construct a family of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation set bifurcations and prevalence. We show that there is a full measure subset of [0, 1], consisting of infinitely many mutually disjoint non-trivial closed intervals, on each of which the rotation set mode lo...
-
作者：Georgakopoulos, Agelos
作者单位：University of Warwick
摘要：Answering a question of Benjamini and Schramm (Ann Probab 24(3):1219-1238, 1996), we show that the Poisson boundary of any planar, uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised geometrically as a circle, which arises from a discrete version of Riemann's mapping theorem. This implies a conjecture of Northshield (Potential Anal 2(4):299-314, 1993). Some of our technique apply to the non-planar case and might have further applications. When the graph...
