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Revisiting Noether's Theorem on constants of motion
Gianluca Gorni, Gaetano Zampieri
In this paper we revisit Noether's theorem on the constants of motion for Lagrangian mechanical systems in the ODE case, with some new perspectives on both the theoretical and the…
Global isochronous potentials
Gianluca Gorni, Gaetano Zampieri
We present a geometric characterization of the nonlinear smooth functions for which the origin is a global isochronous center for the scalar equation .…
On cubic-linear polynomial mappings
Gianluca Gorni, Gaetano Zampieri
In the field of the Jacobian conjecture it is well-known after Druzkowski that from a polynomial "cubic-homogeneous" mapping we can build a higher-dimensional "cubic-linear" mappin…
Reducing scattering problems under cone potentials to normal form by global canonical transformations
Gianluca Gorni, Gaetano Zampieri
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" , , by means of a global canonical transformation $ (P,Q)=A(p,q…
Complete Integrability for Hamiltonian Systems with a Cone Potential
Gianluca Gorni, Gaetano Zampieri
It is known that, if a point in is driven by a bounded below potential , whose gradient is always in a closed convex cone which contains no lines, then the velocity has a…
Liouville-Arnold integrability for scattering under cone potentials
Gianluca Gorni, Gaetano Zampieri
The problem of scattering of particles on the line with repulsive interactions, gives rise to some well-known integrable Hamiltonian systems, for example, the nonperiodic Toda latt…
A class of integrable Hamiltonian systems including scattering of particles on the line with repulsive interactions
Gianluca Gorni, Gaetano Zampieri
The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a la…