Luigi Chierchia
Largo San Leonardo Murialdo 1, I - 00146 Roma, Italy
Dip di Matematica e Fisica, Università Roma Tre
Publications:
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Chierchia L., Koudjinan C.
V. I. Arnold's “Pointwise” KAM Theorem
2019, vol. 24, no. 6, pp. 583-606
Abstract
We review V.I. Arnold's 1963 celebrated paper [1] Proof of A.N. Kolmogorov's Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold's scheme, one can get ''sharp'' asymptotic quantitative conditions (as $\varepsilon \to 0$, $\varepsilon$ being the strength of the perturbation). All constants involved are explicitly computed.
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Chierchia L.
Meeting Jürgen Moser
2009, vol. 14, no. 1, pp. 5-6
Abstract
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Chierchia L.
Kolmogorov’s 1954 Paper on Nearly-Integrable Hamiltonian Systems
2008, vol. 13, no. 2, pp. 130-139
Abstract
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.
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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
Abstract
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.
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