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On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems
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-JacobiExpand
A new method for measuring the splitting of invariant manifolds
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 aExpand
Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
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 whoseExpand
Resurgent functions and splitting problems
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 theExpand
Introduction to 1-summability and resurgence
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 transformExpand
Divergent Series, Summability and Resurgence I: Monodromy and Resurgence
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 differentialExpand
Borel summation and splitting of separatrices for the Hénon map
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 ofExpand
Borel-Laplace Summation
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 astronomersExpand
Mould expansions for the saddle-node and resurgence monomials
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 anExpand
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 separatrixExpand