C*-Algebras Associated with Complex Dynamical Systems and Backward Orbit Structure

Tsuyoshi Kajiwara, Yasuo Watatani

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)

抄録

Let R be a rational function. The iterations (Rn)n of R gives a complex dynamical system on the Riemann sphere. We associate a C*-algebra and study a relation between the C*-algebra and the original complex dynamical system. In this short note, we recover the number of n th backward orbits counted without multiplicity starting at branched points in terms of associated C*-algebras with gauge actions. In particular, we can partially imagine how a branched point is moved to another branched point under the iteration of R. We use KMS states and a Perron-Frobenius type operator on the space of traces to show it.

本文言語英語
ページ(範囲)243-254
ページ数12
ジャーナルComplex Analysis and Operator Theory
8
1
DOI
出版ステータス出版済み - 1 2014

All Science Journal Classification (ASJC) codes

  • 計算数学
  • 計算理論と計算数学
  • 応用数学

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