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Zap. Nauchn. Sem. POMI, 2003, Volume 300, Pages 25–55 (Mi znsl961)  

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

Splitting of separatrices for the Chirikov standard map

V. F. Lazutkin


Abstract: This paper is an English translation (made by V. Gelfreich) of V. F. Lazutkin's work that was published in 1984 by VINITI and thus was not easily available for readers. In the paper, a formula for an exponentially small angle of separatrix splitting of the Chirikov standard map was obtained for the first time.

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English version:
Journal of Mathematical Sciences (New York), 2005, 128:2, 2687–2705

Bibliographic databases:

UDC: 534
Received: 11.11.1984
Language:

Citation: V. F. Lazutkin, “Splitting of separatrices for the Chirikov standard map”, Representation theory, dynamical systems. Part VIII, Special issue, Zap. Nauchn. Sem. POMI, 300, POMI, St. Petersburg, 2003, 25–55; J. Math. Sci. (N. Y.), 128:2 (2005), 2687–2705

Citation in format AMSBIB
\Bibitem{Laz03}
\by V.~F.~Lazutkin
\paper Splitting of separatrices for the Chirikov standard map
\inbook Representation theory, dynamical systems. Part~VIII
\bookinfo Special issue
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 300
\pages 25--55
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl961}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1993024}
\zmath{https://zbmath.org/?q=an:1120.37039}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 2
\pages 2687--2705
\crossref{https://doi.org/10.1007/s10958-005-0219-7}


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

    This publication is cited in the following articles:
    1. Valdes A.D.I., “Poincaré, creator of still-modern methods in differential equations and in celestial mathematics”, Arbor-Ciencia Pensamiento Y Cultura, 178:704 (2004), 669–689  isi
    2. Gelfreich V., Simo C., “High-precision computations of divergent asymptotic series and homoclinic phenomena”, Discrete and Continuous Dynamical Systems-Series B, 10:2–3 (2008), 511–536  mathscinet  zmath  isi
    3. Gelfreich V., Naudot V., “Width of the Homoclinic Zone in the Parameter Space for Quadratic Maps”, Experimental Mathematics, 18:4 (2009), 409–427  crossref  mathscinet  zmath  isi  elib  scopus
    4. Martinez R., Simo C., “Non-integrability of Hamiltonian systems through high order variational equations: Summary of results and examples”, Regular & Chaotic Dynamics, 14:3 (2009), 323–348  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Guardia M., Olive C., Seara T.M., “Exponentially Small Splitting for the Pendulum: A Classical Problem Revisited”, J Nonlinear Sci, 20:5 (2010), 595–685  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Stenlund M., “An Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum”, J. Math. Phys., 51:7 (2010), 072902  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Simo C., Vieiro A., “Dynamics in chaotic zones of area preserving maps: Close to separatrix and global instability zones”, Physica D-Nonlinear Phenomena, 240:8 (2011), 732–753  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    8. Martin P., Sauzin D., Seara T.M., “Exponentially Small Splitting of Separatrices in the Perturbed Mcmillan Map”, Discrete and Continuous Dynamical Systems, 31:2 (2011), 301–372  crossref  mathscinet  zmath  isi  scopus
    9. 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  mathnet  crossref  mathscinet  zmath
    10. Delshams A. Gonchenko M. Gutierrez P., “Exponentially Small Lower Bounds For the Splitting of Separatrices To Whiskered Tori With Frequencies of Constant Type”, Int. J. Bifurcation Chaos, 24:8 (2014), 1440011  crossref  mathscinet  zmath  isi  elib  scopus
    11. Delshams A. Gonchenko M. Gutierrez P., “Exponentially Small Asymptotic Estimates For the Splitting of Separatrices To Whiskered Tort With Quadratic and Cubic Frequencies”, Electron. Res. Announc. Math. Sci., 21 (2014), 41–61  crossref  mathscinet  zmath  isi
    12. Delshams A. Gonchenko M. Gutierrez P., “Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio”, SIAM J. Appl. Dyn. Syst., 15:2 (2016), 981–1024  crossref  mathscinet  zmath  isi  elib  scopus
    13. Baldoma I., Castejon O., Seara T.M., “Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (i)”, J. Nonlinear Sci., 28:5 (2018), 1551–1627  crossref  mathscinet  isi  scopus
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