86 citations · 197 across the 14 of their papers we have counts for
14 papers
On potentials whose level sets are orbits
Philippe Bolle, Marco Mazzucchelli, Andrea Venturelli
A level orbit of a mechanical Hamiltonian system is a solution of Newton equation that is contained in a level set of the potential energy. In 2003, Mark Levi asked for a character…
Quasi-periodic solutions of nonlinear wave equations on the d-dimensional torus
Massimiliano Berti, Philippe Bolle
The main result of this research Monograph is the existence of small amplitude time quasi-periodic solutions for autonomous nonlinear wave equations $$ u_{tt} - Δu + V(x) u + g(x,…
Tonelli Hamiltonians without conjugate points and integrability
Marc Arcostanzo, Marie-Claude Arnaud, Philippe Bolle +1
We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $T^*\T^n$ of the -dimensional torus that have no conjugate points are integrable, i.e. $T^*\T^n$…
Sobolev quasi periodic solutions of multidimensional wave equations with a multiplicative potential
Massimiliano Berti, Philippe Bolle
We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodical…
Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential
Massimiliano Berti, Philippe Bolle
We prove the existence of quasi-periodic solutions for Schroedinger equations with a multiplicative potential on T^d, d \geq 1, merely differentiable nonlinearities, and tangential…
Cantor families of periodic solutions for completely resonant nonlinear wave equations
M. Berti, P. Bolle
We prove existence of small amplitude, $2π\slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequen…