38 citations · 123 across the 18 of their papers we have counts for
20 papers
Perturbation theory of the quadratic Lotka-Volterra double center
Jean-Pierre Françoise, Lubomir Gavrilov
We revisit the bifurcation theory of the Lotka-Volterra quadratic system \begin{eqnarray} X_0 :\left\{\begin{aligned} \dot{x}=& - y -x^2+y^2 ,\\ \dot{y}= &\;\;\;\;x - 2xy \end{alig…
The Rigid Body Dynamics in an ideal fluid: Clebsch Top and Kummer surfaces
Jean-Pierre Francoise, Daisuke Tarama
This is an expository presentation of a completely integrable Hamiltonian system of Clebsch top under a special condition introduced by Weber. After a brief account on the geometri…
Hilbert's 16th problem on a period annulus and Nash space of arcs
Jean-Pierre Françoise, Lubomir Gavrilov, Dongmei Xiao
This article introduces an algebro-geometric setting for the space of bifurcation functions involved in the local Hilbert's 16th problem on a period annulus. Each possible bifurcat…
Analytic Extension of the Birkhoff Normal Forms for the Free Rigid Body Dynamics on SO(3)
Jean-Pierre Francoise, Daisuke Tarama
Birkhoff normal form is a power series expansion associated with the local behavior of the Hamiltonian systems near a critical point. It is known to be convergent for integrable sy…
Inversion of a mapping associated with the Aomoto-Forrester system
Raquel Caseiro, Jean-Pierre Françoise, Ryu Sasaki
This article is devoted to the study of a general class of Hamiltonian systems which extends the Calogero systems with external quadratic potential associated to any root system. T…
Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle
Jean Pierre Francoise, Pedro Garrido, Giovanni Gallavotti
Revisiting canonical integration of the classical solid near a uniform rotation, canonical action angle coordinates, hyperbolic and elliptic, are constructed in terms of various po…