HYPERBOLICITY AND THE CREATION OF HOMOCLINIC ORBITS
HYPERBOLICITY AND THE CREATION OF HOMOCLINIC ORBITS
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双曲线性和同宿轨道的产生
DOI：
10.2307/1971313
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发表时间：
1987
影响因子：
4.9
通讯作者：
F. Takens
中科院分区：
文献类型：
--
作者：
J. Palis;F. Takens
我们考虑曲面上的单参数单同态族{sp，; t E R}，这些曲面对yt = 0显示同宿相切，对yt < 0显示双曲（即，(pf有一个双曲非游荡集）;正切展开到横截同宿轨道的yt积极的。对于这些家庭中的许多人，我们证明，（p也是双曲的最小的正值的yt（这意味着许多规则性的动力学结构）。一个主要的假设涉及的极限容量的基本设置对应的同宿切线。
We consider one-parameter families {sp,; t E R} of diffeomorphisms on surfaces which display a homoclinic tangency for yt = 0 and are hyperbolic for yt < 0 (i.e., (pf has a hyperbolic nonwandering set); the tangency unfolds into transversal homoclinic orbits for yt positive. For many of these families, we prove that (p is also hyperbolic for most small positive values of yt (which implies much regularity of the dynamical structure). A main assumption concerns the limit capacities of the basic set corresponding to the homoclinic tangency.