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We consider the plane 3 body problem with 2 of the masses small. Periodic solutions with near collisions of small bodies were named by Poincaré second species periodic solutions. Such solutions… (More)

We prove the existence of a number of smooth periodic motions u∗ of the classical Newtonian N–body problem which, up to a relabeling of the N particles, are invariant under the rotation group R of… (More)

We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal tickness of the stratum we show the… (More)

We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\mu>0$… (More)

- Paolo Buttà, Piero Negrini
- 2010

We rigorously prove the existence of directed transport for a certain class of ac-driven nonlinear one dimensional systems, namely the generation of transport with a preferred direction in the… (More)

- Piero Negrini
- 1995

- Piero Negrini
- 2011

We discuss the classical problem of the stability of the stationary solution ψ∗ = − cos y for the Euler equation on a 2-dimensional flat torus of sides 2πL and 2π. We prove that ψ∗ is linearly stable… (More)