Annals of Mathematics

最新文章

• On the distribution of matrix elements for the quantum cat map AI翻译
  作者：Kurlberg, P; Rudnick, Z
  摘要：For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study the fluctuations of the matrix elements for the desymmetrized quantum cat map. We present a conjecture for the distribution of the normalized matrix elements, namely that their distribution is that of a certain weighted sum of traces of independent matrices in...
• Curve shortening and the topology of closed geodesics on surfaces AI翻译
  作者：Angenent, SB
  摘要：We study flat knot types of geodesics on compact surfaces M-2. For every flat knot type and any Riemannian metric g we introduce a Conley index associated with the curve shortening flow on the space of immersed curves on M-2. We conclude existence of closed geodesics with prescribed flat knot types, provided the associated Conley index is nontrivial.
• Formation of singularities for a transport equation with nonlocal velocity AI翻译
  作者：Córdoba, A; Córdoba, D; Fontelos, MA
  摘要：We study a ID transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.
• On the hardness of approximating minimum vertex cover AI翻译
  作者：Dinur, I; Safra, S
  摘要：We prove the Minimum Vertex Cover problem to be NP-hard to approximate to within a factor of 1.3606, extending on previous PCP and hardness of approximation technique. To that end, one needs to develop a new proof framework, and to borrow and extend ideas from several fields.
• Equidistribution of special sub-varieties AI翻译
  作者：Clozel, L; Ullmo, E
• On Paley-Wiener's theorem on Arthur AI翻译
  作者：Delorme, P
  摘要：The Fourier transform of a C-infinity function, f, with compact support on a real reductive Lie group G is given by a collection of operators phi(P, sigma, lambda) := pi(P)(sigma, lambda) (f) for a suitable family of representations of G, which depends on a family, indexed by P in a finite set of parabolic subgroups of G, of pairs of parameters (sigma, lambda), sigma varying in a set of discrete series, lambda lying in a complex finite dimensional vector space. The pi(P)(sigma, lambda) are gen...
• Twisted Fermat curves over totally real fields AI翻译
  作者：Diaconu, A; Tian, Y
• The classification of torsion endo-trivial modules AI翻译
  作者：Carlson, JF; Thévenaz, J
• Decay of geometry for unimodal maps: negative Schwarzian case AI翻译
  作者：Graczyk, J; Sands, D; Swiatek, G
  摘要：We show that decay of geometry holds for unimodal maps of the interval which have negative Schwarzian derivative, sufficient finite smoothness, and a nondegenerate critical point. The proof is based on pseudo-analytic extensions of order at least 2. They allow us to modify Sullivan's principle that rescaled high iterates of one-dimensional maps tend to analytic limits in such a way that no passage to a limit is actually needed, but the maps are shown to approach the analytic class in a well de...
• A resolution of the K(2)-local sphere at the prime 3 AI翻译
  作者：Goerss, P; Henn, HW; Mahowald, M; Rezk, C
  摘要：We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum L-K(2) S-0 as the inverse limit of a tower of fibrations with four layers. The successive fibers are of the form E-2(hF) where F is a finite subgroup of the Morava stabilizer group and E-2 is the second Morava or Lubin-Tate homology theory. We give explicit calculation of the homotopy groups of these fibers. The ca...