|
Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
On the 75th birthday of Professor L.P. Shilnikov
Shilnikov’s cross-map method and hyperbolic dynamics of three-dimensional Hénon-like maps
S. Gonchenkoa, M.-Ch. Lib a Research Institute of Applied Mathematics and Cybernetics,
Nizhny Novgorod State University, Russia
b Department of Applied Mathematics and Center of Mathematical Modelling and Scientific Computing, National Chiao Tung University, Hsinchu, Taiwan
Аннотация:
We study the hyperbolic dynamics of three-dimensional quadratic maps with constant Jacobian the inverse of which are again quadratic maps (the so-called 3D Hénon maps). We consider two classes of such maps having applications to the nonlinear dynamics and find certain sufficient conditions under which the maps possess hyperbolic nonwandering sets topologically conjugating to the Smale horseshoe. We apply the so-called Shilnikov’s crossmap for proving the existence of the horseshoes and show the existence of horseshoes of various types: (2,1)- and (1,2)-horseshoes (where the first (second) index denotes the dimension of stable (unstable) manifolds of horseshoe orbits) as well as horseshoes of saddle and saddle-focus types.
Ключевые слова:
quadratic map, Smale horseshoe, hyperbolic set, symbolic dynamics, saddle, saddlefocus.
Поступила в редакцию: 11.11.2009 Принята в печать: 12.02.2010
Образец цитирования:
S. Gonchenko, M.-Ch. Li, “Shilnikov’s cross-map method and hyperbolic dynamics of three-dimensional Hénon-like maps”, Regul. Chaotic Dyn., 15:2-3 (2010), 165–184
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd486 https://www.mathnet.ru/rus/rcd/v15/i2/p165
|
Статистика просмотров: |
Страница аннотации: | 87 |
|