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On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems

- P. Lochak, Jean-Pierre Marco, D. Sauzin
- Mathematics
- 2003

Introduction and some salient features of the model Hamiltonian Symplectic geometry and the splitting of invariant manifolds Estimating the splitting matrix using normal forms The Hamilton-Jacobi… Expand

A new method for measuring the splitting of invariant manifolds

- D. Sauzin
- Mathematics
- 1 March 2001

We study the so-called Generalized Arnol'd Model (a weakly hyperbolic near-integrable Hamiltonian system), with d+1 degrees of freedom (d⩾2), in the case where the perturbative term does not affect a… Expand

Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems

- Jean-Pierre Marco, D. Sauzin
- Mathematics
- 1 May 2003

Abstract. – We prove a theorem about the stability of action variables for Gevrey quasi-convex near-integrable Hamiltonian systems and construct in that context a system with an unstable orbit whose… Expand

Resurgent functions and splitting problems

- D. Sauzin
- Mathematics
- 1 June 2007

The present text is an introduction to \'Ecalle's theory of resurgent functions and alien calculus, in connection with problems of exponentially small separatrix splitting. An outline of the… Expand

Introduction to 1-summability and resurgence

- D. Sauzin
- Mathematics
- 2 May 2014

This text is about the mathematical use of certain divergent power series. The rst part is an introduction to 1-summability. The denitions rely on the formal Borel transform and the Laplace transform… Expand

Divergent Series, Summability and Resurgence I: Monodromy and Resurgence

- C. Mitschi, D. Sauzin
- Mathematics
- 11 December 2016

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential… Expand

Borel summation and splitting of separatrices for the Hénon map

- V. Gelfreich, D. Sauzin
- Mathematics
- 2001

We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Henon map. A single formal power series corresponds to both of them. The Borel transform of… Expand

Borel-Laplace Summation

- D. Sauzin
- Mathematics
- 2016

At the beginning of the second volume of his New methods of celestial mechanics [Poi87], H. Poincar´e dedicates two pages to elucidating “a kind of misunderstanding between geometers and astronomers… Expand

Mould expansions for the saddle-node and resurgence monomials

- D. Sauzin
- Mathematics
- 14 December 2007

This article is an introduction to some aspects of \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an… Expand

RESURGENCE OF INNER SOLUTIONS FOR PERTURBATIONS OF THE MCMILLAN MAP

- Pau Martín, D. Sauzin, M. Alonso
- Mathematics
- 1 June 2011

A sequence of "inner equations" attached to certain perturbations of the
McMillan map was considered in [5], their solutions were used
in that article to measure an exponentially small separatrix… Expand

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