U. Locatelli, A. Giorgilli, “Construction of Kolmogorov's normal form for a planetary system”, Regul. Chaotic Dyn., 10:2 (2005), 153

Regular and Chaotic Dynamics

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Regular and Chaotic Dynamics, 2005, Volume 10, Issue 2, Pages 153–171
DOI: https://doi.org/10.1070/RD2005v010n02ABEH000309 (Mi rcd704)

This article is cited in 25 scientific papers (total in 25 papers)

150th anniversary of H. Poincaré

Construction of Kolmogorov's normal form for a planetary system

U. Locatelli^a, A. Giorgilli^b

^a Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy
^b Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano Bicocca, Via R. Cozzi 53, 20125 Milano, Italy

Citations (25)

DOI: https://doi.org/10.1070/RD2005v010n02ABEH000309

Abstract: We describe an algorithm constructing an invariant KAM torus for a class of planetary systems, such that the mutual attractions, the eccentricities and the inclinations of the planets are small enough. By using computer algebra, we explicitly implement this algorithm for approximating a KAM torus for the problem of three bodies in a case similar to the Sun–Jupiter–Saturn system. We show that, by reducing the masses of the planets by a factor 10 and with a small displacement of the orbits, our semianalytical construction of the torus turns out to be successful.

Keywords: three-body problem, $n$-body problem, KAM theory, perturbation methods, Hamiltonian systems, celestial mechanics.

Received: 06.04.2005
Accepted: 03.06.2005

Bibliographic databases:

Document Type: Article

MSC: 70F07, 70F10, 37J40, 37N05, 70–08, 70H08

Language: English

Citation: U. Locatelli, A. Giorgilli, “Construction of Kolmogorov's normal form for a planetary system”, Regul. Chaotic Dyn., 10:2 (2005), 153–171

Citation in format AMSBIB

\Bibitem{LocGio05}

\by U.~Locatelli, A. Giorgilli

\paper Construction of Kolmogorov's normal form for a planetary system

\jour Regul. Chaotic Dyn.

\yr 2005

\vol 10

\issue 2

\pages 153--171

\mathnet{http://mi.mathnet.ru/rcd704}

\crossref{https://doi.org/10.1070/RD2005v010n02ABEH000309}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2159013}

\zmath{https://zbmath.org/?q=an:1128.70304}

Linking options:

https://www.mathnet.ru/eng/rcd704

https://www.mathnet.ru/eng/rcd/v10/i2/p153

This publication is cited in the following 25 articles:

Jordi-Lluís Figueras, Alex Haro, “Sun–Jupiter–Saturn System May Exist: A Verified Computation of Quasiperiodic Solutions for the Planar Three-Body Problem”, J Nonlinear Sci, 35:1 (2025)
Veronica Danesi, Ugo Locatelli, Marco Sansottera, “Existence proof of librational invariant tori in an averaged model of HD60532 planetary system”, Celest Mech Dyn Astron, 135:3 (2023)
Marco Sansottera, Veronica Danesi, “Kolmogorov variation: KAM with knobs (à la Kolmogorov)”, MINE, 5:5 (2023), 1
Xuefeng Zhao, Yong Li, “KAM in Generalized Hamiltonian Systems with Multi-Scales”, J Dyn Diff Equat, 35:4 (2023), 2971
Alessandra Celletti, Encyclopedia of Complexity and Systems Science, 2023, 1
Alessandra Celletti, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2022, 339
Àngel Jorba, Encyclopedia of Complexity and Systems Science Series, Perturbation Theory, 2022, 153
Àngel Jorba, Encyclopedia of Complexity and Systems Science, 2022, 1
Alessandra Celletti, Encyclopedia of Complexity and Systems Science, 2022, 1
Antonio Giorgilli, Ugo Locatelli, Marco Sansottera, “Secular Dynamics of a Planar Model of the Sun-Jupiter-Saturn-Uranus System; Effective Stability in the Light of Kolmogorov and Nekhoroshev Theories”, Regul. Chaotic Dyn., 22:1 (2017), 54–77
Àlex Haro, Alejandro Luque, Applied Mathematical Sciences, 195, The Parameterization Method for Invariant Manifolds, 2016, 119
Letizia Stefanelli, Ugo Locatelli, “Quasi-periodic motions in a special class of dynamical equations with dissipative effects: A pair of detection methods”, DCDS-B, 20:4 (2015), 1155
M. Sansottera, U. Locatelli, A. Giorgilli, “On the stability of the secular evolution of the planar Sun–Jupiter–Saturn–Uranus system”, Mathematics and Computers in Simulation, 88 (2013), 1
Anne-Sophie Libert, Marco Sansottera, “On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems”, Celest Mech Dyn Astr, 117:2 (2013), 149
Alessandra Celletti, Mathematics of Complexity and Dynamical Systems, 2012, 1301
Marco Sansottera, Ugo Locatelli, Antonio Giorgilli, “A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems”, Celest Mech Dyn Astr, 111:3 (2011), 337
Alessandra Celletti, “Some KAM applications to Celestial Mechanics”, Discrete & Continuous Dynamical Systems - S, 3:4 (2010), 533
Yuecai Han, Yong Li, Yingfei Yi, “Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy”, Ann. Henri Poincaré, 10:8 (2010), 1419
Elena Lega, Massimiliano Guzzo, Claude Froeschlé, “A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems”, Celest Mech Dyn Astr, 107:1-2 (2010), 129
E. Lega, M. Guzzo, C. Froeschlé, “Numerical studies of hyperbolic manifolds supporting diffusion in symplectic mappings”, Eur. Phys. J. Spec. Top., 186:1 (2010), 3

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	115

Registration to the website

Logotypes