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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 3(339), Pages 79–142 (Mi umn394)  

This article is cited in 46 scientific papers (total in 46 papers)

Splitting of separatrices: perturbation theory and exponential smallness

V. G. Gelfreicha, V. F. Lazutkin

a Saint-Petersburg State University

Abstract: This is a survey of the main results related to separatrix splitting for area-preserving maps and Hamiltonian systems with one and a half degrees of freedom. Special attention is paid to problems in which the separatrix splitting is exponentially small with respect to the perturbation parameter.


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English version:
Russian Mathematical Surveys, 2001, 56:3, 499–558

Bibliographic databases:

UDC: 517.927+517.928+517.987
MSC: Primary 37J40, 37J45; Secondary 37D10, 37J10, 37C29, 37G20, 34E05, 34C37, 70K40, 7
Received: 23.05.2000

Citation: V. G. Gelfreich, V. F. Lazutkin, “Splitting of separatrices: perturbation theory and exponential smallness”, Uspekhi Mat. Nauk, 56:3(339) (2001), 79–142; Russian Math. Surveys, 56:3 (2001), 499–558

Citation in format AMSBIB
\by V.~G.~Gelfreich, V.~F.~Lazutkin
\paper Splitting of separatrices: perturbation theory and exponential smallness
\jour Uspekhi Mat. Nauk
\yr 2001
\vol 56
\issue 3(339)
\pages 79--142
\jour Russian Math. Surveys
\yr 2001
\vol 56
\issue 3
\pages 499--558

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    This publication is cited in the following articles:
    1. Gelfreich V., “Near strongly resonant periodic orbits in a Hamiltonian system”, Proc. Natl. Acad. Sci. USA, 99:22 (2002), 13975–13979  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
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    7. Loskutov A., Janoe A., “Homoclinical chaos suppression”, International Conference Physics and Control, 1–4, 2003, 403–409  isi
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    24. Gelfreich V., Gelfreikh N., “Unique resonant normal forms for area-preserving maps at an elliptic fixed point”, Nonlinearity, 22:4 (2009), 783–810  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
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    34. José Pedro Gaivão, Vassili Gelfreich, “Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift–Hohenberg equation as an example”, Nonlinearity, 24:3 (2011), 677  crossref  mathscinet  zmath  isi  scopus  scopus
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    40. Vassili Gelfreich, Lev Lerman, “Separatrix Splitting at a Hamiltonian $0^2 i\omega$ Bifurcation”, Regul. Chaotic Dyn., 19:6 (2014), 635–655  mathnet  crossref  mathscinet  zmath
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    45. Fontich E., Simo C., Vieiro A., “Splitting of the Separatrices After a Hamiltonian-Hopf Bifurcation Under Periodic Forcing”, Nonlinearity, 32:4 (2019), 1440–1493  crossref  mathscinet  zmath  isi  scopus
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