Zobrazeno 1 - 10
of 68
pro vyhledávání: '"Luigi Chierchia"'
Autor:
Luca Biasco, Luigi Chierchia
In this note we present and briefly discuss results, which include as a particular case the theorem announced in [L. Biasco, and L. Chierchia. On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems. Atti Accad. Naz. Lince
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ca96564a3ae8febe17314ac5a7927f63
This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the Whitney c
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74378655fb41895db66a500ba8d01d4a
Autor:
Luigi Chierchia, Luca Biasco
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -). 197:261-281
From KAM theory it follows that the measure of phase points which do not lie on Diophantine, Lagrangian, “primary” tori in a nearly integrable, real-analytic Hamiltonian system is \(O(\sqrt{\varepsilon })\), if \(\varepsilon \) is the size of the
Autor:
Luigi Chierchia, Luca Biasco
A conjecture of Arnold, Kozlov and Neishtadt on the exponentially small measure of the "non-torus" set in analytic systems with two degrees of freedom is discussed.
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d89f33b46961c85d83b4124e6d098951
We review V.I. Arnold's 1963 celebrated paper \cite{ARV63} {\sl Proof of A.N. Kolmogorov's theorem on the conservation of conditionally periodic motions with a small variation in the Hamiltonian}, and prove that, optimizing Arnold's scheme, one can g
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0a14d894a1f6eee51c8010c65d258337
Autor:
Luigi Chierchia, Luca Biasco
We show that, in general, averaging at simple resonances a real-analytic, nearly-integrable Hamiltonian, one obtains a one-dimensional system with a cosine-like potential; 'in general' means for a generic class of holomorphic perturbations and apart
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We consider geometric properties of 3-jet non-degenerate functions in connection with Nekhoroshev theory. In particular, after showing that 3-jet non-degenerate functions are “almost quasi-convex”, we prove that they are steep and compute explici
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::07c8b442424d6f3f4d37a694ebc4f142
https://hdl.handle.net/11590/351174
https://hdl.handle.net/11590/351174
Autor:
Luigi Chierchia, Luca Biasco
Publikováno v:
Rendiconti Lincei - Matematica e Applicazioni. 26:423-432
Consider an n-degrees-of-freedom real-analytic mechanical system with potential $\epsilon f = \epsilon f(x)$, x being a n-dimensional angle variable. Then, for ‘‘general’’ potentials f ’s and $\epsilon$ small enough, the Liouville measure o
Autor:
Luigi Chierchia, Gabriella Pinzari
Publikováno v:
Celestial Mechanics and Dynamical Astronomy
Celestial Mechanics and Dynamical Astronomy, Springer Verlag, 2011, 109 (3), pp.285-301. ⟨10.1007/s10569-010-9329-8⟩
Celestial Mechanics and Dynamical Astronomy, Springer Verlag, 2011, 109 (3), pp.285-301. ⟨10.1007/s10569-010-9329-8⟩
International audience; We revisit a set of symplectic variables introduced by Andre Deprit (Celest Mech , 181-195, 1983), which allows for a complete symplectic reduction in rotation invariant Hamiltonian systems, generalizing to arbitrary dimension
Autor:
Luigi Chierchia, Gabriella Pinzari
Publikováno v:
Journal of Modern Dynamics. 5:623-664
Birkhoff normal forms for the (secular) planetary problem are investigated. Existence and uniqueness is discussed and it is shown that the classical Poincare variables and the ʀᴘs-variables (introduced in [6]), after a trivial lift, lead to the sa