H. Rüssmann, “Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 6:2 (2001), 119

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Regular and Chaotic Dynamics, 2001, Volume 6, Issue 2, Pages 119–204
DOI: https://doi.org/10.1070/RD2001v006n02ABEH000169 (Mi rcd837)

This article is cited in 144 scientific papers (total in 144 papers)

Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems

H. Rüssmann

Fachbereich Mathematik, Universität Mainz, 55099 Mainz, Germany

Citations (144)

DOI: https://doi.org/10.1070/RD2001v006n02ABEH000169

Abstract: Invariant tori for analytic nearly integrable Hamiltonian systems are constructed under rather weak sufficient conditions being even necessary in the case of maximal invariant tori. All small devisors are controlled by a general approximation function the properties of which correspond to the Bruno condition in analytic problems near a singular point. The admitted size of the perturbations is numerically determined in numerically given systems.

Received: 10.03.2001

Bibliographic databases:

Document Type: Article

MSC: 34C27, 37J40, 70H08

Language: English

Citation: H. Rüssmann, “Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 6:2 (2001), 119–204

Citation in format AMSBIB

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\paper Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems

\jour Regul. Chaotic Dyn.

\yr 2001

\vol 6

\issue 2

\pages 119--204

\mathnet{http://mi.mathnet.ru/rcd837}

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1843664}

\zmath{https://zbmath.org/?q=an:0992.37050}

Linking options:

https://www.mathnet.ru/eng/rcd837

https://www.mathnet.ru/eng/rcd/v6/i2/p119

Addendum

Addendum to "Invariant tori in non-degenerate nearly integrable Hamiltonian systems", RCD 6(2) 2001
H. Rüssmann
Regul. Chaotic Dyn., 2005, 10:1, 21–31

This publication is cited in the following 144 articles:

Zineb Hassainia, Emeric Roulley, “Boundary effects on the emergence of quasi-periodic solutions for Euler equations”, Nonlinearity, 38:1 (2025), 015016
Meina Gao, Jianjun Liu, Zejing Liu, “Quasi-periodic solutions around plane wave of high dimensional nonlinear Schrödinger equation”, Journal of Differential Equations, 434 (2025), 113229
Weichao Qian, Xue Yang, Yong Li, “Partial Frequency and Frequency Ratio in Multiscale KAM Formulism”, J Dyn Diff Equat, 2025
Qi Li, Junxiang Xu, “Persistence of a class of degenerate hyperbolic lower dimensional invariant tori in Hamiltonian systems”, Journal of Differential Equations, 433 (2025), 113227
Henk W. Broer, Heinz Hanßmann, Florian Wagener, “Parametrised KAM Theory, an Overview”, Regul. Chaot. Dyn., 2025
Zhicheng Tong, Jiayin Du, Yong Li, “The KAM theorem on the modulus of continuity about parameters”, Sci. China Math., 67:3 (2024), 577
Qi Li, Junxiang Xu, “A Formal KAM Theorem for Hamiltonian Systems and Its Application to Hyperbolic Lower Dimensional Invariant Tori”, Qual. Theory Dyn. Syst., 23:2 (2024)
Xiaomei Yang, Junxiang Xu, “Persistence of the Non-twist Degenerate Lower Dimensional Invariant Torus in Reversible Systems”, Qual. Theory Dyn. Syst., 23:5 (2024)
You Jiangong, “The KAM method for the spectral theory of quasi-periodic Schrödinger operators”, Sci. Sin.-Math., 54:6 (2024), 863
Massimiliano Berti, “KAM for Vortex Patches”, Regul. Chaotic Dyn., 29:4 (2024), 654–676
Abed Bounemoura, Hamiltonian Systems, 2024, 67
Roberto Feola, Jessica Elisa Massetti, “Non-Resonant Conditions for the Klein – Gordon Equation on the Circle”, Regul. Chaotic Dyn., 29:4 (2024), 541–564
Xiaomei Yang, Junxiang Xu, “Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping”, Regul. Chaotic Dyn., 29:4 (2024), 605–619
Zhaowei Lou, “Reducibility of Linear Quasi-periodic Hamiltonian Derivative Wave Equations and Half-Wave Equations Under the Brjuno Conditions”, J Dyn Diff Equat, 2024
Luca Franzoi, Nader Masmoudi, Riccardo Montalto, “Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow”, Arch Rational Mech Anal, 248:5 (2024)
Zineb Hassainia, Taoufik Hmidi, Emeric Roulley, “Invariant KAM Tori Around Annular Vortex Patches for 2D Euler Equations”, Commun. Math. Phys., 405:11 (2024)
Mei Na Gao, Jian Jun Liu, “A Degenerate KAM Theorem for Partial Differential Equations with Unbounded Perturbations”, Acta. Math. Sin.-English Ser., 40:11 (2024), 2719
Jiayin Du, Yong Li, Hongkun Zhang, “Kolmogorov's theorem for degenerate Hamiltonian systems with Hölder continuous parameters”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2024, 1
Zhichao Ma, Junxiang Xu, “Response Solutions for Completely Degenerate Oscillators Under Arbitrary Quasi-Periodic Perturbations”, Commun. Math. Phys., 402:1 (2023), 1
Abed Bounemoura, Gerard Farré, “Positive Measure of Effective Quasi-Periodic Motion Near a Diophantine Torus”, Ann. Henri Poincaré, 24:9 (2023), 3289

Citing articles in Google Scholar: Russian citations, English citations
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