Open AccessPosted Content
Singularities for analytic continuations of germs of Riccati foliations
TLDR
In this article, it was shown that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all germs of holonomy between a fiber and a holomorphic section of the bundle are led to singularities by almost every developed geodesic ray.Abstract:
In this paper we study the problem of analytic extension of germs of holonomy of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the germs of holonomy between a fiber and a holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they are included and dense in the limit set and uncountable, giving another negative answer to a conjecture of Loray.read more
Citations
More filters
Posted Content
Sur les Theoremes I et II de Painleve
TL;DR: In this paper, a lecture on fundamental Painleve's early Theorems on first order ordinary differential equations with many examples is given, along with two conjectures about the global analytic continuation of holonomy maps locally defined by Theorem II.
References
More filters
Journal ArticleDOI
Gibbs measures in ergodic theory
TL;DR: In this article, the concept of a Gibbs measure was introduced, which generalizes the notion of an equilibrium Gibbs distribution in statistical physics, and a wide class of invariant measures for dynamical systems of this kind were constructed.
Journal ArticleDOI
Noncommuting random products
TL;DR: In this paper, the authors consider the problem of determining the asymptotic behavior of a random sequence (i.e., a sequence of independent real valued random variables with a common distribution function) satisfying the strong law of large numbers.
Journal ArticleDOI
Centennial History of Hilbert’s 16th Problem
TL;DR: The second part of Hilbert's 16th problem deals with polynomial differential equations in the plane as mentioned in this paper, and it remains unsolved even for quadratic polynomials.