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Эта публикация цитируется в 53 научных статьях (всего в 53 статьях)
On the 70th birthday of L.P. Shilnikov
Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
S. V. Gonchenkoa, J. D. Meissb, I. I. Ovsyannikovc a Institute for Applied Mathematics and Cybernetics,
10, Uljanova Str. 603005 Nizhny Novgorod, Russia
b Applied Mathematics, University of Colorado,
Boulder, CO 80309
c Radio and Physical Department,
Nizhny Novgorod State University,
23 Gagarin str., 603000 Nizhny Novgorod, Russia
Аннотация:
We study bifurcations of a three-dimensional diffeomorphism, $g_0$, that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers $(\lambda e^{i \varphi}, \lambda e^{-i \varphi}, \gamma)$, where $0< \lambda < 1 <|\gamma|$ and $|\lambda^2 \gamma|=1$. We show that in a three-parameter family, $g_{\varepsilon}$, of diffeomorphisms close to $g_0$, there exist infinitely many open regions near $\varepsilon = 0$ 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 three-dimensional quadratic maps with constant Jacobian.
Ключевые слова:
saddle-focus fixed point, three-dimensional quadratic map, homoclinic bifurcation, strange attractor.
Поступила в редакцию: 03.10.2005 Принята в печать: 12.11.2005
Образец цитирования:
S. V. Gonchenko, J. D. Meiss, I. I. Ovsyannikov, “Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation”, Regul. Chaotic Dyn., 11:2 (2006), 191–212
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd668 https://www.mathnet.ru/rus/rcd/v11/i2/p191
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