Pseudo-abelian integrals: Unfolding generic exponential case

Pseudo-concave Integrals

The notion of Lehrer-concave integral is generalized taking instead of the usual arithmetical operations of addition and multiplication of reals more general real operations called pseudo-addition and pseudomultiplication.

Discrete pseudo-integrals

Article history: Available online 21 August 2012

Motivic Exponential Integrals

Abelian integrals in holomorphic foliations

The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singu...

Stochastic Integrals and Abelian Processes

We study triangulation schemes for the joint kernel of a diffusion process with uniformly continuous coefficients and an adapted, non-resonant Abelian process. The prototypical example of Abelian process to which our methods apply is given by stochastic integrals with uniformly continuous coefficients. The range of applicability includes also a broader class of processes of practical relevance,...