ON THE STABILITY OF THE PERTURBED CENTRAL MOTION PROBLEM: A QUASICONVEXITY AND A NEKHOROSHEV TYPE RESULT
Tesi di Dottorato
Data di Pubblicazione:
2018
Citazione:
ON THE STABILITY OF THE PERTURBED CENTRAL MOTION PROBLEM: A QUASICONVEXITY AND A NEKHOROSHEV TYPE RESULT / A. Fuse' ; relatore: D. P. Bambusi ; coordinatore del dottorato: V. Mastropietro. DIPARTIMENTO DI MATEMATICA "FEDERIGO ENRIQUES", 2018 Mar 26. 30. ciclo, Anno Accademico 2017. [10.13130/fuse-alessandra_phd2018-03-26].
Abstract:
The aim of this thesis is the study of the dynamics of small perturbations of the spatial central motion problem. Our main result consists in proving that if the central potential is
analytic, then, except for the Harmonic and the Keplerian case,
the unperturbed system written in action angle variables is
quasiconvex. Thus, when it is perturbed, one can apply a
Nekhoroshev type theorem ensuring the stability over exponentially
long times of the modulus of the angular momentum and of the energy of the
unperturbed system. Being a \emph{superintegrable} system, namely, a system which admits a number of
independent integrals of motion larger than the number of degrees of
freedom, the version of Nekhoroshev theorem provided here is the one for superintegrable systems. We also give a complete proof (à la Lochak) of this result.
Tipologia IRIS:
Tesi di dottorato
Elenco autori:
A. Fuse'
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