Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

Small Exotic Molecules with Bosonic Constituents

We study the stability and the properties of the ground state of neutral systems containing up to four positively charged bosons and their antiparticles. Examples are the di-pionium molecule (π ⁺ π ⁻)², which is almost identical to the positronium molecule (e ⁺ e ⁻)², the tri-pionium (π ⁺ π ⁻)³, and the quadri-pionium (π ⁺ π ⁻)⁴ molecules. We briefly compare our results on the energy to those on the large-N limit of (π ⁺ π ⁻) ^N . We also show that the annihilation probability can be calculated accurately with simple wave functions when one uses the generalized Schwinger rule. Received September 5, 1994; accepted for publication October 15, 1994     

Non-homogeneous equations of the thermoacoustics: Thermally forced radial thermo-elastic oscillations of the visco-thermal fluid sphere

The purpose of this paper is to solve the coupled non-homogeneous equations derived from the basic classical theory of the acoustic propagation in visco-thermal fluid. The 1D radial distribution of pressure and temperature inside a spherical object was found. It is supposed that both acoustic and thermal conditions on a surface of the object are known. The starting equations are considered in the time domain and their solution was found without initial conditions for steady harmonic motion.     

Sur les automorphismes analytiques des variétés hyperboliques

Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism.