Displaying similar documents to “Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle”

Perturbative expansions in quantum mechanics

Mauricio D. Garay (2009)

Annales de l’institut Fourier

Similarity:

We prove a D = 1 analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg algebra. The quantised version of the Morse lemma already shows that the perturbation series arising in a perturbed harmonic oscillator become analytic after a formal Borel transform.

On q -summation and confluence

Lucia Di Vizio, Changgui Zhang (2009)

Annales de l’institut Fourier

Similarity:

This paper is divided in two parts. In the first part we study a convergent q -analog of the divergent Euler series, with q ( 0 , 1 ) , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding q -difference equation. In the second part, we work under the assumption q ( 1 , + ) . In this case, at least four different q -Borel sums of a divergent power series solution of an irregular...

Complex vector fields and hypoelliptic partial differential operators

Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten (2010)

Annales de l’institut Fourier

Similarity:

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which...

Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand, Maciej Zworski (2007)

Annales de l’institut Fourier

Similarity:

We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators...

Geometry of currents, intersection theory and dynamics of horizontal-like maps

Tien-Cuong Dinh, Nessim Sibony (2006)

Annales de l’institut Fourier

Similarity:

We introduce a geometry on the cone of positive closed currents of bidegree ( p , p ) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like mappings. The Green currents satisfy some extremality properties. The equilibrium measure is invariant, mixing and has maximal entropy. It is equal to the intersection of the Green currents associated to the horizontal-like map and to its inverse.