## Abstract

We study fractional quadratic transformations T of the sphere and try to determine their topological entropy. In the case where T is a constant mapping or a homeomorphism, the topological entropy is of course zero. In the other cases, we have the following results. If T has only one fixed point, its entropy is log 2. If T has exactly two fixed points, it can be written as T_{z}=z-z^{-1}+v, and if v is real, then the entropy of T is again log 2. A general result of Misiurewicz and Przytycki shows that the entropy of T is at least log2, and we conjecture that this entropy is always equal to log2 in the remaining cases, i. e. two fixed points and v not real, and three fixed points.

Translated title of the contribution | A remark on topological entropy |
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Original language | German |

Pages (from-to) | 177-183 |

Number of pages | 7 |

Journal | Monatshefte für Mathematik |

Volume | 85 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1978 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)