Abstract:
A complete description of dynamics in a neighborhood of a finite bunch of homoclinic loops to a saddle equilibrium state of a Hamiltonian system is given.
Keywords:
Hamiltonian system, nonintegrability and chaos, resonance crossing, Arnold diffusion.
Citation:
Dmitry Turaev, “Hyperbolic Sets near Homoclinic Loops to a Saddle for Systems with a First Integral”, Regul. Chaotic Dyn., 19:6 (2014), 681–693
\Bibitem{Tur14}
\by Dmitry~Turaev
\paper Hyperbolic Sets near Homoclinic Loops to a Saddle for Systems with a First Integral
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 681--693
\mathnet{http://mi.mathnet.ru/rcd191}
\crossref{https://doi.org/10.1134/S1560354714060069}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3284608}
\zmath{https://zbmath.org/?q=an:06507826}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000345996200006}
Linking options:
https://www.mathnet.ru/eng/rcd191
https://www.mathnet.ru/eng/rcd/v19/i6/p681
This publication is cited in the following 3 articles:
Sajjad Bakrani, Jeroen S.W. Lamb, Dmitry Turaev, “Invariant manifolds of homoclinic orbits and the dynamical consequences of a super-homoclinic: A case study in R4 with Z2-symmetry and integral of motion”, Journal of Differential Equations, 327 (2022), 1
Lerman L.M. Trifonov K.N., “Saddle-Center and Periodic Orbit: Dynamics Near Symmetric Heteroclinic Connection”, Chaos, 31:2 (2021), 023113
S. V. Bolotin, D. V. Treschev, “The anti-integrable limit”, Russian Math. Surveys, 70:6 (2015), 975–1030
Citation in format AMSBIB
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