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Uspekhi Mat. Nauk, 1989, Volume 44, Issue 2(266), Pages 49–78 (Mi umn2273)  

This article is cited in 14 scientific papers (total in 14 papers)

Normalization of a Hamiltonian system near an invariant cycle or torus

A. D. Bruno


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English version:
Russian Mathematical Surveys, 1989, 44:2, 53–89

Bibliographic databases:

UDC: 517.93
MSC: 37J40, 70H12
Received: 26.06.1987

Citation: A. D. Bruno, “Normalization of a Hamiltonian system near an invariant cycle or torus”, Uspekhi Mat. Nauk, 44:2(266) (1989), 49–78; Russian Math. Surveys, 44:2 (1989), 53–89

Citation in format AMSBIB
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\by A.~D.~Bruno
\paper Normalization of a Hamiltonian system near an invariant cycle or torus
\jour Uspekhi Mat. Nauk
\yr 1989
\vol 44
\issue 2(266)
\pages 49--78
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\zmath{https://zbmath.org/?q=an:0696.34020}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1989RuMaS..44...53B}
\transl
\jour Russian Math. Surveys
\yr 1989
\vol 44
\issue 2
\pages 53--89
\crossref{https://doi.org/10.1070/RM1989v044n02ABEH002041}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Amadeu Delshams, Teresa M. Seara, “An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum”, Comm Math Phys, 150:3 (1992), 433  crossref  mathscinet  zmath  isi
    2. M. B. Sevryuk, “New cases of quasiperiodic motions in reversible systems”, Chaos, 3:2 (1993), 211  crossref  mathscinet  zmath  adsnasa  isi
    3. G. R. W. Quispel, M. B. Sevryuk, “KAM theorems for the product of two involutions of different types”, Chaos, 3:4 (1993), 757  crossref  mathscinet  zmath  adsnasa
    4. S. I. Pidkuiko, “On the massiveness of the set of nonintegrable Hamiltonians”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 515–532  mathnet  crossref  mathscinet  zmath  isi
    5. M. B. Sevryuk, “The iteration-approximation decoupling in the reversible KAM theory”, Chaos, 5:3 (1995), 552  crossref  mathscinet  zmath  adsnasa  isi
    6. A A Zevin, Nonlinearity, 12:5 (1999), 1339  crossref  mathscinet  zmath  adsnasa  isi
    7. Àlex Haro, “An algorithm to generate canonical transformations: application to normal forms”, Physica D: Nonlinear Phenomena, 167:3-4 (2002), 197  crossref
    8. Mercè Ollé, Juan R Pacha, Jordi Villanueva, “Quantitative estimates on the normal form around a non-semi-simple 1:−1 resonant periodic orbit”, Nonlinearity, 18:3 (2005), 1141  crossref  mathscinet  zmath  isi
    9. Mercè Ollé, Juan R Pacha, Jordi Villanueva, “Kolmogorov–Arnold–Moser aspects of the periodic Hamiltonian Hopf bifurcation”, Nonlinearity, 21:8 (2008), 1759  crossref  elib
    10. Alejandro Luque, Jordi Villanueva, “A KAM theorem without action-angle variables for elliptic lower dimensional tori”, Nonlinearity, 24:4 (2011), 1033  crossref
    11. Guillermo Dávila-Rascón, Yuri Vorobiev, “Hamiltonian structures for projectable dynamics on symplectic fiber bundles”, DCDS-A, 33:3 (2012), 1077  crossref
    12. A. Yu. Anikin, “Librations and ground-state splitting in a multidimensional double-well problem”, Theoret. and Math. Phys., 175:2 (2013), 609–619  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Lev Lerman, Anna Markova, “Symmetric Homoclinic Orbits at the Periodic Hamiltonian Hopf Bifurcation”, Int. J. Bifurcation Chaos, 24:08 (2014), 1440006  crossref
    14. A. I. Neishtadt, D. V. Treschev, “Dinamicheskie effekty, svyazannye s poterei ustoichivosti polozhenii ravnovesiya i periodicheskikh traektorii”, UMN, 76:5(461) (2021), 147–194  mathnet  crossref
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