Eine bemerkung zur topologischen entropie

Translated title of the contribution: A remark on topological entropy

Manfred Heinz Denker, Michael S. Keane

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 Tz=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 contributionA remark on topological entropy
Original languageGerman
Pages (from-to)177-183
Number of pages7
JournalMonatshefte für Mathematik
Volume85
Issue number3
DOIs
StatePublished - Sep 1 1978

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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