Infinite-modal maps with global chaotic behavior
Infinite-modal maps with global chaotic behavior
复制标题
具有全局混沌行为的无限模态映射
DOI：
10.2307/121002
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
M. Viana
中科院分区：
文献类型：
--
作者：
M. Pacifico;A. Rovella;M. Viana
证明了具有无穷多个临界点的一维参数化映射族具有持续的全局混沌行为：对于参数的正Lebesgu型测度集，映射是可传递的，且几乎每个轨道都有正的Lyapunov指数.这些方法的应用给出了三维光滑流动的整体螺旋吸引子的存在性甚至持久性的证明，将在[5]中给出。
We prove that certain parametrized families of one-dimensional maps with infinitely many critical points exhibit global chaotic behavior in a persistent way: For a positive Lebesgue measure set of parameter values the map is transitive and almost every orbit has positive Lyapunov exponent. An application of these methods yields a proof of existence and even persistence of global spiral attractors for smooth flows in three dimensions, to be given in [5].