Related papers: Unique resonant normal forms for area preserving m…

We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves…

We study the exponentially small splitting of separatrices in an analytic one-parameter family of area-preserving maps that generically unfolds a 1:3 resonance. Near the resonance the normal form theory predicts existence of a small…

The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The…

We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.

This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical approaches such as wavelets and Radon transforms by…

We derive a fixed-point formula for integrals on moduli spaces of stable maps to projective spaces of even dimension. This gives a formula for the equivariant open Gromov-Witten invariants of (RP^{2m},CP^{2m}) and the structure constants of…

We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and…

Infinitely renormalizable H\'enon-like map in arbitrary finite dimension is considered. The set, $\mathcal N$ of infinitely renormalizable H\'enon-like maps satisfying the certain condition is invariant under renormalization operator. The…

Let $D$ be a bounded strongly convex domain with smooth boundary in $\mathbb C^N$. Let $(\phi_t)$ be a continuous semigroup of holomorphic self-maps of $D$. We prove that if $p\in \partial D$ is an isolated boundary regular fixed point for…

We discuss the local behaviour of vector fields in the plane $\R^2$ around a regular singular point, using recently introduced reduced normal forms, i.e. Poincar\'e and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997),…

In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using…

We complete the list of normal forms for effective 3-forms with constant coefficients with respect to the natural action of symplectomorphisms in \mathbb{R}^6. We show that the 3-form which corresponds to the Special Lagrangian equation is…

An exceptional point in the moduli space of compact Riemann surfaces is a unique surface class whose full automorphism group acts with a triangular signature. A surface admitting a conformal involution with quotient an elliptic curve is…

Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called…

The problem of characterizing GKLS-generators and CP-maps with an invariant appeared in different guises in the literature. We prove two unifying results which hold even for weakly closed *-algebras: First, we show how to construct a normal…

We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…

The Jaynes-Cummings-Gaudin model describes a collection of $n$ spins coupled to an harmonic oscillator. It is known to be integrable, so one can define a moment map which associates to each point in phase-space the list of values of the…