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One of the most beautiful theorems in the theory of dynamical systems is the Sharkovski Theorem. An interval map may have many different periodic points with seemingly unrelated periodicities. What is unexpected and, in fact, amazing is that those periodicities are actually oredered in a certain way, called the Sharkovski orderingSharkovski ordering. The “top chain of the ordering” consists of all odd integers, with the number 3 at the zenith, and the “bottom chain of the ordering” consists of all decreasing powers of 2 , with the number 1 at the nadir.

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Ordering Among Periods: The Sharkovski Theorem

  • 章节

  • 发表日期：

    2025年

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  • Liangliang Li,
  • Yu Huang,
  • Goong Chen

摘要

One of the most beautiful theorems in the theory of dynamical systems is the Sharkovski Theorem. An interval map may have many different periodic points with seemingly unrelated periodicities. What is unexpected and, in fact, amazing is that those periodicities are actually oredered in a certain way, called the Sharkovski orderingSharkovski ordering. The “top chain of the ordering” consists of all odd integers, with the number 3 at the zenith, and the “bottom chain of the ordering” consists of all decreasing powers of 2 , with the number 1 at the nadir.