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Luigi Chierchia

Largo San Leonardo Murialdo 1, I - 00146 Roma, Italy
Sezione di Matematica, Università Roma Tre


Chierchia L.
Meeting Jürgen Moser
2009, vol. 14, no. 1, pp.  5-6
Citation: Chierchia L.,  Meeting Jürgen Moser, Regular and Chaotic Dynamics, 2009, vol. 14, no. 1, pp. 5-6
Chierchia L.
Kolmogorov’s 1954 Paper on Nearly-Integrable Hamiltonian Systems
2008, vol. 13, no. 2, pp.  130-139
Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of integrable Hamiltonian systems by including few "straightforward" estimates.
Keywords: Kolmogorov’s theorem, KAM theory, small divisors, Hamiltonian systems, perturbation theory, symplectic transformations, nearly-integrable systems
Citation: Chierchia L.,  Kolmogorov’s 1954 Paper on Nearly-Integrable Hamiltonian Systems, Regular and Chaotic Dynamics, 2008, vol. 13, no. 2, pp. 130-139
Celletti A., Chierchia L.
Construction of stable periodic orbits for the spin-orbit problem of celestial mechanics
1998, vol. 3, no. 3, pp.  107-121
Birkhoff periodic orbits associated to spin-orbit resonances in Celestial Mechanics and in particular to the Moon–Earth and Mercury–Sun systems are considered. A general method (based on a quantitative version of the Implicit Function Theorem) for the construction of such orbits with particular attention to "effective estimates" on the size of the perturbative parameters is presented and tested on the above mentioned systems. Lyapunov stability of the periodic orbits (for small values of the perturbative parameters) is proved by constructing KAM librational invariant surfaces trapping the periodic orbits.
Citation: Celletti A., Chierchia L.,  Construction of stable periodic orbits for the spin-orbit problem of celestial mechanics, Regular and Chaotic Dynamics, 1998, vol. 3, no. 3, pp. 107-121

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