The dynamics of magnetic flows for energies above Mane's critical value

We show that, for energies above Mane's critical value, minimal magnetic geodesics are Riemannian (A,0)-quasi-geodesics where A -> 1 as the energy tends to infinity. As a consequence, on negatively curved manifolds, minimal magnetic geodesics lie in tubes around Riemannian geodesics. Finally, we investigate a natural metric introduced by Mane via the so-called action potential. Although this magnetic metric does depend on the magnetic field, the associated magnetic length turns out to be just the Riemannian length

Copula Theory: An Introduction

Abstract In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have been applie

Copula theory: an introduction

In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have been applied in various fields, and several methods of constructing multivariate copulas