ar X iv : m at h / 04 07 11 4 v 3 [ m at h . D S ] 2 4 Ja n 20 05 STATISTICAL STABILITY OF SADDLE - NODE ARCS

ar X iv : m at h / 04 07 11 4 v 4 [ m at h . D S ] 3 0 N ov 2 00 5 STATISTICAL STABILITY OF SADDLE - NODE ARCS

We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical and stochastic stability results for deterministic and random perturbations in this kind of one-parameter families. CONTENTS

ar X iv : m at h / 04 07 11 4 v 1 [ m at h . D S ] 8 J ul 2 00 4 STATISTICAL STABILITY OF SADDLE - NODE ARCS

We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical stability results for deterministic and random perturbations in these kind of one-parameter families. In the process we characterize the asymptotic dynamics of Lebesgue almost every point for maps f near the bifurcation value and obtain equili...

ar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION

ar X iv : m at h / 04 10 33 5 v 2 [ m at h . C O ] 3 1 Ja n 20 05 HIGHER CONNECTIVITY OF GRAPH COLORING COMPLEXES

The main result of this paper is a proof of the following conjecture of Babson & Kozlov: Theorem. Let G be a graph of maximal valency d, then the complex Hom (G, Kn) is at least (n − d − 2)-connected. Here Hom (−,−) denotes the polyhedral complex introduced by Lovász to study the topological lower bounds for chromatic numbers of graphs. We will also prove, as a corollary to the main theorem, th...

ar X iv : m at h / 04 02 15 2 v 2 [ m at h . Q A ] 1 4 Ja n 20 05 On relations for the q - multiple zeta values

We prove some relations for the q-multiple zeta values (qMZV). They are q-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the dimension of the space spanned by qMZV's over Q, and present an application to MZV.