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

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)243-254
Number of pages12
JournalComplex Analysis and Operator Theory
Issue number1
Publication statusPublished - Jan 2014


  • Backward orbit
  • Branched point
  • C-algebra
  • C-correspondences
  • Complex dynamical system

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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