The statements and reports mathematics

We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature – in fact, we only assume that the geodesic flow has the Anosov property. In the semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics. 1. Introduction, statement of results We consider a compact Riemannian manifold M of dimension d ≥ 2, and assume that the geodesic flow (g t )t∈R , acting on the unit tangent bundle of M , has a “chaotic”...

43p dontetvui 17-01-2013 54 7   Download

Introduction and statement of results Let E ⊂ Rn , and m ≥ 1. We write C m (E) for the Banach space of all real-valued functions ϕ on E such that ϕ = F on E for some F ∈ C m (Rn ). The natural norm on C m (E) is given by ϕ C m (E) = inf{ F C m (Rn ) : F ∈ C m (Rn ) and F = ϕ on E} . Here, as usual, C m (Rn ) is the space of real-valued functions on Rn with continuous and bounded derivatives through order m; and F C m (Rn ) = |β|≤m x∈Rn max sup |∂ β F (x)| .

58p noel_noel 17-01-2013 53 6   Download

We prove the topological (or combinatorial) rigidity property for real polynomials with all critical points real and nondegenerate, which completes the last step in solving the density of Axiom A conjecture in real one-dimensional dynamics. Contents 1. Introduction 1.1. Statement of results 1.2. Organization of this work 1.3. General terminologies and notation 2. Density of Axiom A follows from the Rigidity Theorem 3. Derivation of the Rigidity Theorem from the Reduced Rigidity Theorem

94p noel_noel 17-01-2013 47 8   Download

A Hausdorff measure version of the Duffin-Schaeffer conjecture in metric number theory is introduced and discussed. The general conjecture is established modulo the original conjecture. The key result is a Mass Transference Principle which allows us to transfer Lebesgue measure theoretic statements for lim sup subsets of Rk to Hausdorff measure theoretic statements. In view of this, the Lebesgue theory of lim sup sets is shown to underpin the general Hausdorff theory. This is rather surprising since the latter theory is viewed to be a subtle refinement of the former. ...

23p noel_noel 17-01-2013 48 6   Download

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry.

55p noel_noel 17-01-2013 61 7   Download

Consider the inverse eigenvalue problem of the Schr¨dinger operator deo fined on a finite interval. We give optimal and almost optimal conditions for a set of eigenvalues to determine the Schr¨dinger operator. These conditions are o simple closedness properties of the exponential system corresponding to the known eigenvalues. The statements contain nearly all former results of this topic. We give also conditions for recovering the Weyl-Titchmarsh m-function from its values m(λn ).

35p noel_noel 17-01-2013 43 6   Download

We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction. 1. Introduction and statement of the results Let (M, g) be a compact Riemannian manifold with boundary ∂M . Let dg (x, y) denote the geodesic distance between x and y. The inverse problem we address in this paper is whether we can determine the Riemannian metric g knowing dg (x, y) for any x ∈ ∂M , y ∈ ∂M . ...

19p noel_noel 17-01-2013 41 3   Download

We prove that any genus-2 Lefschetz fibration without reducible fibers and with “transitive monodromy” is holomorphic. The latter condition comprises all cases where the number of singular fibers µ ∈ 10N is not congruent to 0 modulo 40. This proves a conjecture of the authors in [SiTi1]. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S 2 -bundles over S 2 , of relative degree ≤ 7 over the base, and of symplectic surfaces in CP2 of degree ≤ 17. ...

63p noel_noel 17-01-2013 48 5   Download

Statement of the main result. Denote by Δ(r) the disk of radius r in C, Δ := Δ(1), and for 0

44p tuanloccuoi 04-01-2013 44 7   Download

We classify the measure theoretic attractors of general C 3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry. 1. Introduction 1.1. Statement of results. The study of measure theoretical attractors occupied a central position in the theory of smooth dynamical systems in the 1990s. Recall that a forward invariant compact set A is called a (minimal) metric attractor for some dynamics if the basin of attraction B(A) := {x : ω(x) ⊂ A} of A has positive Lebesgue measure and B(A ) has Lebesgue measure zero for every forward invariant compact set...

17p tuanloccuoi 04-01-2013 45 6   Download

In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

37p thulanh8 19-09-2011 58 14   Download

Spectral extrema for graphs: the Zarankiewicz problem L´szl´ Babai∗ a o Barry Guiduli†Submitted: Jul 12, 2007; Accepted: Sep 21, 2009; Published: Sep 25, 2009 Abstract Let G be a graph on n vertices with spectral radius λ (this is the largest eigenvalue of the adjacency matrix of G). We show that if G does not contain the complete bipartite graph Kt,s as a subgraph, where 2 t s, then λ (s − 1)1/t + o(1) n1−1/t for fixed t and s while n → ∞. Asymptotically, this bound matches the K˝v´rio a Tur´n-S´s upper bound on the average degree of G...

8p thulanh8 19-09-2011 57 7   Download

Tham khảo luận văn - đề án 'research report: "the propagation of ultrashort pulses keer environment."', luận văn - báo cáo phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

8p phalinh14 07-08-2011 71 4   Download