Henon-like maps with strange attractors: there exist C? Kupka-Smale diffeomorphisms on S2 with neither sinks nor sources
Henon-like maps with strange attractors: there exist C? Kupka-Smale diffeomorphisms on S2 with neither sinks nor sources
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带有奇怪吸引子的类似 Henon 的映射：存在 C？
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
C. Tresser
中科院分区：
文献类型：
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作者：
J. Gambaudo;S. Strein;C. Tresser
证明了S2上无周期汇和周期源的CinnamoKupka-Smale同态的存在性。这样，他们就对Smale在1962年提出的一个问题得到了完整的回答。Bowen，Franks和Young（1976）以前已经构造了C2例子。它们的构造表明，在一般的Cinnamon单参数族中，存在具有非双曲奇异吸引子的映射。这些族包括Henon族（x，y）到（1-ax 2 +y，bx）。(In定理的陈述，它们描述了它们所指的奇怪吸引子）。此外，作为他们的方法的副产品，他们得到了第一个例子，Cinnamoorphisms，这都是在一个级联的倍周期分岔的积累和边界的Morse-Smale系统。证明了所有这些映射都有一个非游荡集，这个非游荡集与相应的一维映射的非游荡集共轭。
The authors prove the existence of Cinfinity Kupka-Smale diffeomorphisms on S2 with no periodic sinks or sources. Thus they obtain a complete answer to a question raised by Smale in 1962. Bowen, Franks and Young (1976) have previously constructed C2 examples. Their construction shows that in generic Cinfinity one-parameter families there exist maps which have a non-hyperbolic strange attractor. These families include the Henon family (x,y) to (1-ax2+y,bx). (In the statements of the theorems they describe what they mean by a strange attractor). Also, as a by-product of their method, they get the first examples of Cinfinity diffeomorphisms which are both at the accumulation of a cascade of period-doubling bifurcations and at the boundary of Morse-Smale systems. They show that all these maps have a non-wandering set which is conjugate to the non-wandering set of the corresponding one-dimensional map.