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

Tsuyoshi Kajiwara, Yasuo Watatani

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume8
Issue number1
DOIs
Publication statusPublished - Jan 1 2014

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Complex Dynamical Systems
Algebra
C*-algebra
Dynamical systems
Orbits
Orbit
KMS States
Perron-Frobenius
Iteration
Rational functions
Rational function
Gages
Multiplicity
Gauge
Trace
Operator

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

C*-Algebras Associated with Complex Dynamical Systems and Backward Orbit Structure. / Kajiwara, Tsuyoshi; Watatani, Yasuo.

In: Complex Analysis and Operator Theory, Vol. 8, No. 1, 01.01.2014, p. 243-254.

Research output: Contribution to journalArticle

Kajiwara, Tsuyoshi ; Watatani, Yasuo. / C*-Algebras Associated with Complex Dynamical Systems and Backward Orbit Structure. In: Complex Analysis and Operator Theory. 2014 ; Vol. 8, No. 1. pp. 243-254.
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