Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation

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dc.creatorGonchenko, S. V.
dc.creatorMeiss, J. D.
dc.creatorOvsyannikov, I. I.
dc.date2005-10-24
dc.date.accessioned2026-07-07T08:10:55Z
dc.date.available2026-07-07T08:10:55Z
dc.descriptionWe study bifurcations of a three-dimensional diffeomorphism, $g_0$, that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers $(λe^{i\vphi}, λe^{-i\vphi}, γ)$, where $0<λ<1<|γ|$ and $|λ^2γ|=1$. We show that in a three-parameter family, $g_{\eps}$, of diffeomorphisms close to $g_0$, there exist infinitely many open regions near $\eps =0$ where the corresponding normal form of the first return map to a neighborhood of a homoclinic point is a three-dimensional Hénon-like map. This map possesses, in some parameter regions, a "wild-hyperbolic" Lorenz-type strange attractor. Thus, we show that this homoclinic bifurcation leads to a strange attractor. We also discuss the place that these three-dimensional Hénon maps occupy in the class of quadratic volume-preserving diffeomorphisms.
dc.descriptionlaTeX, 25 pages, 6 eps figures
dc.identifierhttps://arxiv.org/abs/nlin/0510061
dc.identifierhttp://arxiv.org/abs/nlin/0510061
dc.identifierReg. & Chaotic Dyn. 11(2) 191-212 (2006)
dc.identifierdoi:10.1070/RD2006v011n02ABEH000345
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131963
dc.subjectChaotic Dynamics
dc.titleChaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
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