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Bounded topological speedups

机译:有界的拓扑加速

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摘要

This paper explores the range of bounded speedups in the topological category. Bounded speedups represent both a strengthening of topological speedups as first defined by the second author, and a generalization of powers of a transformation. Here we show that bounded speedups preserve the structure of two classical minimal Cantor systems. Specifically, a minimal bounded speedup of an odometer is a conjugate odometer, and a minimal bounded speedup of a primitive substitution is again a primitive substitution, though it is never conjugate to the original substitution system. Further, we give bounds on the topological entropy of bounded speedups, and in special cases, we compute the topological entropy of bounded speedups.
机译:本文探讨了拓扑类别中有界加速的范围。有界加速比既代表第二作者首先定义的拓扑加速比的增强,又代表变换的幂的泛化。在这里,我们显示出有界加速比保留了两个经典的最小Cantor系统的结构。具体而言,里程表的最小有界加速是共轭里程表,而原始替换的最小有界加速仍然是原始替换,尽管它从未与原始替换系统共轭。此外,我们对有界加速的拓扑熵给出了界限,在特殊情况下,我们计算了有界加速的拓扑熵。

著录项

  • 来源
    《Dynamical Systems》 |2018年第2期|303-331|共29页
  • 作者单位

    Department of Mathematics, Bradley University, Peoria, IL, USA;

    Department of Mathematics and Computer Science, Davidson College, Davidson, NC, USA;

    Department of Mathematics, University of Denver, Denver, CO, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Topological speedups; odometers; substitutions; Kakutani-Rokhlin towers; entropy;

    机译:拓扑加速;里程表;替代;Kakutani-Rokhlin塔;熵;

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