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The Smale horseshoeSmale horseshoe offers a model for pervasive high-dimensional nonlinear phenomena, as well as a powerful technique for proving chaos. Here in this chapter, we present the famous Smale horseshoe and show that it has a shift invariant set with respect to the two-sided shift. We first introduce the standard Smale horseshoe and then discuss the general case.

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The Smale Horseshoe

  • 章节

  • 发表日期：

    2025年

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  • Liangliang Li,
  • Yu Huang,
  • Goong Chen

摘要

The Smale horseshoeSmale horseshoe offers a model for pervasive high-dimensional nonlinear phenomena, as well as a powerful technique for proving chaos. Here in this chapter, we present the famous Smale horseshoe and show that it has a shift invariant set with respect to the two-sided shift. We first introduce the standard Smale horseshoe and then discuss the general case.