Real polynomials

We study unitary random matrix ensembles of the form −1 Zn,N | det M |2α e−N Tr V (M ) dM, where α −1/2 and V is such that the limiting mean eigenvalue density for n, N → ∞ and n/N → 1 vanishes quadratically at the origin. In order to compute the double scaling limits of the eigenvalue correlation kernel near the origin, we use the Deift/Zhou steepest descent method applied to the Riemann-Hilbert problem for orthogonal polynomials on the real line with respect to the weight |x|2α e−N V (x) . ...

42p dontetvui 17-01-2013 79 8   Download

Annals of Mathematics In this paper we will solve one of the central problems in dynamical systems: Theorem 1 (Density of hyperbolicity for real polynomials). Any real polynomial can be approximated by hyperbolic real polynomials of the same degree. Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of infinity.

39p noel_noel 17-01-2013 52 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 52 9   Download

We prove that almost every nonregular real quadratic map is ColletEckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic maps have excellent ergodic properties, as exponential decay of correlations (Keller and Nowicki, Young) and stochastic stability in the strong sense (Baladi and Viana). This is an important step in achieving the same results for more general families of unimodal maps.

52p noel_noel 17-01-2013 62 6   Download

This is the second of two papers in which we prove the Tits alternative for Out(Fn ). Contents 1. Introduction and outline 2. Fn -trees 2.1. Real trees 2.2. Real Fn -trees 2.3. Very small trees 2.4. Spaces of real Fn -trees 2.5. Bounded cancellation constants 2.6. Real graphs 2.7. Models and normal forms for simplicial Fn -trees 2.8. Free factor systems 3. Unipotent polynomially growing outer automorphisms 3.1. Unipotent linear maps 3.2. Topological representatives 3.3. Relative train tracks and automorphisms of polynomial growth 3.4. Unipotent representatives and UPG automorphisms ...

60p noel_noel 17-01-2013 49 7   Download

This paper deals with some questions about the dynamics of diffeomorphisms of R2 . A “model family” which has played a significant historical role in dynamical systems and served as a focus for a great deal of research is the family introduced by H´non, which may be written as e fa,b (x, y) = (a − by − x2 , x) b = 0.

27p tuanloccuoi 04-01-2013 45 7   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: q-Eulerian polynomials and polynomials with only real zeros...

9p thulanh6 15-09-2011 57 2   Download