4 citations · 9 across the 12 of their papers we have counts for
20 papers
A new class of separable Lagrangian systems generalizing Sawada-Kotera
Gianluca Gorni, Mattia Scomparin, Gaetano Zampieri
Some characteristics of the Sawada-Kotera Lagrangian system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom.
The geodesics for Poincaré's half-plane: a nonstandard derivation
Gianluca Gorni, Gaetano Zampieri
Constants of motion are usually derived from groups of symmetry transformation of the system. Here we show that useful properties of the system can be deduced from a family of Noet…
Nonlocal constants of motion in Lagrangian Dynamics of any order
Gianluca Gorni, Mattia Scomparin, Gaetano Zampieri
We describe a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechani…
Lagrangian dynamics by nonlocal constants of motion
Gianluca Gorni, Gaetano Zampieri
A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in t…
A quasi separable dissipative Maxwell-Bloch system for laser dynamics
Gianluca Gorni, Stefania Residori, Gaetano Zampieri
The Maxwell-Bloch dissipative equations describe laser dynamics. Under a simple condition on the parameters there exist two time dependent first integrals, that allow a nonstandard…
Applications of nonlocal constants of motion in Lagrangian Dynamics
Gianluca Gorni, Gaetano Zampieri
We give a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems and we apply the method to find useful constants of motion for dissipative system, for the La…
Global Inversion of Functions: an Introduction
Giuseppe De Marco, Gianluca Gorni, Gaetano Zampieri
This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differe…
On-flow and strong solutions to Killing-type equations
Gianluca Gorni, Gaetano Zampieri
If we impose infinitesimal invariance up to a boundary term of the action functional for Lagrangian ordinary differential equations, we are led to Killing-type equations, which are…
Involutions of real intervals
Gaetano Zampieri
This paper shows a simple construction of the continuous involutions of real intervals in terms of the continuous even functions. We also study the smooth involutions defined by sy…
Weak instability of Hamiltonian equilibria
Gaetano Zampieri
This is an expository paper on Lyapunov stability of equilibria of autonomous Hamiltonian systems. Our aim is to clarify the concept of weak instability, namely instability without…
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 .…
Diffeomorphisms with Banach space domains
Gaetano Zampieri
Our basic element is a mapping , with Banach spaces, and with derivative everywhere invertible. So is a local diffeomorphism at every point. The aim of th…
Nonholonomic versus vakonomic dynamics
Gaetano Zampieri
The main aim of the present paper is to raise the doubt that vakonomic dynamics may not be satisfactory as a model for velocity dependent constraints.
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…
Completely integrable Hamiltonian systems with weak Lyapunov instability or isochrony
Gaetano Zampieri
The aim of this paper is to introduce a class of Hamiltonian autonomous systems in dimension 4 which are completely integrable and their dynamics is described in all details. They…