A. V. Pronin, D. V. Treschev, “Continuous Averaging in Multi-frequency Slow-fast Systems”, Regul. Chaotic Dyn., 5:2 (2000), 157

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Regular and Chaotic Dynamics, 2000, Volume 5, Issue 2, Pages 157–170
DOI: https://doi.org/10.1070/RD2000v005n02ABEH000138 (Mi rcd869)

This article is cited in 12 scientific papers (total in 13 papers)

Continuous Averaging in Multi-frequency Slow-fast Systems

A. V. Pronin^a, D. V. Treschev^b

^a Moscow State University, Vorob'ievy Gory, V 10-50, Main Building, 119899, Moscow, Russia
^b Faculty of Mechanics and Mathematics, Department of Theoretical Mechanics, Moscow State University, Vorob'ievy Gory, 119899, Moscow, Russia

Citations (13)

DOI: https://doi.org/10.1070/RD2000v005n02ABEH000138

Abstract: It is well-known that in real-analytic multi-frequency slow-fast ODE systems the dependence of the right-hand sides on fast angular variables can be reduced to an exponentially small order by a near-identical change of the variables. Realistic constructive estimates for the corresponding exponentially small terms are obtained.

Received: 12.12.1999

Bibliographic databases:

Document Type: Article

MSC: 34C15, 34C20, 58F27, 70H05

Language: English

Citation: A. V. Pronin, D. V. Treschev, “Continuous Averaging in Multi-frequency Slow-fast Systems”, Regul. Chaotic Dyn., 5:2 (2000), 157–170

Citation in format AMSBIB

\Bibitem{ProTre00}

\by A. V. Pronin, D. V. Treschev

\paper Continuous Averaging in Multi-frequency Slow-fast Systems

\jour Regul. Chaotic Dyn.

\yr 2000

\vol 5

\issue 2

\pages 157--170

\mathnet{http://mi.mathnet.ru/rcd869}

\crossref{https://doi.org/10.1070/RD2000v005n02ABEH000138}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1780707}

\zmath{https://zbmath.org/?q=an:0977.34040}

Linking options:

https://www.mathnet.ru/eng/rcd869

https://www.mathnet.ru/eng/rcd/v5/i2/p157

This publication is cited in the following 13 articles:

S. V. Bolotin, O. E. Zubelevich, V. V. Kozlov, S. B. Kuksin, A. I. Neishtadt, “Dmitrii Valerevich Treschev (k shestidesyatiletiyu so dnya rozhdeniya)”, UMN, 80:1(481) (2025), 165–170
A. I. Neishtadt, D. V. Treschev, “Dynamical phenomena connected with stability loss of equilibria and periodic trajectories”, Russian Math. Surveys, 76:5 (2021), 883–926
Delshams A. Gonchenko M. Gutierrez P., “Exponentially Small Splitting of Separatrices Associated to 3D Whiskered Tori With Cubic Frequencies”, Commun. Math. Phys., 378:3 (2020), 1931–1976
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez, “Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio”, SIAM J. Appl. Dyn. Syst., 15:2 (2016), 981
Jinxin Xue, “Continuous averaging proof of the Nekhoroshev theorem”, Discrete & Continuous Dynamical Systems - A, 35:8 (2015), 3827
Christian Kuehn, Applied Mathematical Sciences, 191, Multiple Time Scale Dynamics, 2015, 239
Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez, “Continuation of the Exponentially Small Transversality for the Splitting of Separatrices to a Whiskered Torus with Silver Ratio”, Regul. Chaotic Dyn., 19:6 (2014), 663–680
Pere Gutiérrez, Marina Gonchenko, Amadeu Delshams, “Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies”, ERA-MS, 21 (2014), 41
Oleg Zubelevich, “On Analytic Solutions to the Navier-Stokes Equation in 3-D Torus”, FE, 50:2 (2007), 171
Fuzhong Cong, “The approximate decomposition of exponential order of slow–fast motions in multifrequency systems”, Journal of Differential Equations, 196:2 (2004), 466
J. Math. Sci. (N. Y.), 128:2 (2005), 2726–2746
J. Math. Sci. (N. Y.), 128:2 (2005), 2839–2842
O. È. Zubelevich, “On the Majorant Method for the Cauchy–Kovalevskaya Problem”, Math. Notes, 69:3 (2001), 329–339

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

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