Abstract

We study a generalized Hénon map in two-dimensional space. We find a region of the phase space where the nonwandering set exists, specify parameter values for which this nonwandering set is hyperbolic, and prove that our map when restricted to a specific invariant subset is topologically conjugate to the Bernoulli three-shift. Coupling two such maps, as a result, we obtain a map in four-dimensional space and show that Bernoulli shifts also exist in this map.

中文翻译：

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立方 Hénon 映射中的复杂行为

摘要

我们研究二维空间中的广义 Hénon 映射。我们找到非游荡集存在的相空间区域，指定该非游荡集为双曲线的参数值，并证明我们的映射在限制为特定不变子集时与伯努利三移拓扑共轭。将两个这样的映射耦合，结果，我们获得了一个四维空间的映射，并表明该映射中也存在伯努利位移。