A. Celletti, C. Falcolini, U. Locatelli, “On the break-down threshold of invariant tori in four dimensional maps”, Regul. Chaotic Dyn., 9:3 (2004), 227

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Regular and Chaotic Dynamics, 2004, Volume 9, Issue 3, Pages 227–253
DOI: https://doi.org/10.1070/RD2004v009n03ABEH000278 (Mi rcd744)

This article is cited in 15 scientific papers (total in 15 papers)

Effective computations in modern dynamics

On the break-down threshold of invariant tori in four dimensional maps

A. Celletti^a, C. Falcolini^b, U. Locatelli^a

^a Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma (Italy)
^b Dipartimento di Matematica, Università di Roma Tre, Largo S. L. Murialdo 1, I-00146 Roma (Italy)

Citations (15)

DOI: https://doi.org/10.1070/RD2004v009n03ABEH000278

Abstract: We investigate the break-down of invariant tori in a four dimensional standard mapping for different values of the coupling parameter. We select various two-dimensional frequency vectors, having eventually one or both components close to a rational value. The dynamics of this model is very reach and depends on two parameters, the perturbing and coupling parameters. Several techniques are introduced to determine the analyticity domain (in the complex perturbing parameter plane) and to compute the break-down threshold of the invariant tori. In particular, the analyticity domain is recovered by means of a suitable implementation of Padé approximants. The break-down threshold is computed through a suitable extension of Greene's method to four dimensional systems. Frequency analysis is implemented and compared with the previous techniques.

Received: 27.09.2004

Bibliographic databases:

Document Type: Article

MSC: 70K55, 37J10, 65P40, 70K43

Language: English

Citation: A. Celletti, C. Falcolini, U. Locatelli, “On the break-down threshold of invariant tori in four dimensional maps”, Regul. Chaotic Dyn., 9:3 (2004), 227–253

Citation in format AMSBIB

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\by A.~Celletti, C.~Falcolini, U.~Locatelli

\paper On the break-down threshold of invariant tori in four dimensional maps

\jour Regul. Chaotic Dyn.

\yr 2004

\vol 9

\issue 3

\pages 227--253

\mathnet{http://mi.mathnet.ru/rcd744}

\crossref{https://doi.org/10.1070/RD2004v009n03ABEH000278}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2104170}

\zmath{https://zbmath.org/?q=an:1102.70011}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9..227C}

Linking options:

https://www.mathnet.ru/eng/rcd744

https://www.mathnet.ru/eng/rcd/v9/i3/p227

This publication is cited in the following 15 articles:

Adrián P. Bustamante, “Computation of domains of analyticity of lower dimensional tori in a weakly dissipative Froeschlé map”, Communications in Nonlinear Science and Numerical Simulation, 142 (2025), 108538
Adrian P. Bustamante, Alessandra Celletti, Christoph Lhotka, “Breakdown of rotational tori in 2D and 4D conservative and dissipative standard maps”, Physica D: Nonlinear Phenomena, 453 (2023), 133790
Alessandra Celletti, Joan Gimeno, Mauricio Misquero, “The Spin–Spin Problem in Celestial Mechanics”, J Nonlinear Sci, 32:6 (2022)
Stoeber J., Baecker A., “Geometry of Complex Instability and Escape in Four-Dimensional Symplectic Maps”, Phys. Rev. E, 103:4 (2021), 042208
Sander E., Meiss J.D., “Birkhoff Averages and Rotational Invariant Circles For Area-Preserving Maps”, Physica D, 411 (2020), 132569
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
J.-Ll. Figueras, A. Haro, A. Luque, “Rigorous Computer-Assisted Application of KAM Theory: A Modern Approach”, Found Comput Math, 17:5 (2017), 1123
J. D. Meiss, “Thirty years of turnstiles and transport”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25:9 (2015)
Renato C. Calleja, Alessandra Celletti, Corrado Falcolini, Rafael de la Llave, “An Extension of Greene's Criterion for Conformally Symplectic Systems and a Partial Justification”, SIAM J. Math. Anal., 46:4 (2014), 2350
Timothy Blass, Rafael de la Llave, “The Analyticity Breakdown for Frenkel-Kontorova Models in Quasi-periodic Media: Numerical Explorations”, J Stat Phys, 150:6 (2013), 1183
Adam M. Fox, James D. Meiss, “Greene's residue criterion for the breakup of invariant tori of volume-preserving maps”, Physica D: Nonlinear Phenomena, 243:1 (2013), 45
Alessandra Celletti, “Some Aspects of Conservative and Dissipative KAM Theorems”, Milan J. Math., 80:1 (2012), 25
J.D. Meiss, “The destruction of tori in volume-preserving maps”, Communications in Nonlinear Science and Numerical Simulation, 17:5 (2012), 2108
Gemma Huguet, Rafael de la Llave, Yannick Sire, “Computation of whiskered invariant tori and their associated manifolds: New fast algorithms”, Discrete & Continuous Dynamical Systems - A, 32:4 (2012), 1309
Alessandra Celletti, Lecture Notes in Physics, 729, Topics in Gravitational Dynamics, 2007, 67

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

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