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C*-Algebras Associated with \(F_{2^n }\) Unimodal Dynamical Systems

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Abstract

We consider C*-algebras associated with simple unimodal one-dimensional ambiguous dynamical systems \(\left( {f,\mathbb{R}} \right)\) with certain special restrictions. For these algebras, we present a complete classification of irreducible representations in Hilbert spaces and describe the dual space. As an example, we consider the one-parameter family f μ(x) = μx(1 − x).

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REFERENCES

  1. V. Ostrovskyi and Yu. Samoilenko, Introduction to the Theory of Representations of Finitely-Presented *-Algebras. I. Representations by Bounded Operators, Gordon and Breach, Amsterdam (1999).

    Google Scholar 

  2. A. N. Sharkovskii, Yu. L. Maistrenko, and E. Yu. Romanenko, Difference Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  3. L. Jonker and D. Rand, “Bifurcations in one dimension. I, II,” Invent. Math., 62, 347–365; 65, 1–16 (1981).

    Google Scholar 

  4. S. V. Popovych and T. Yu. Maistrenko, “C*-algebras associated with quadratic dynamical system,” in: Proceedings of the Third International Conference on Symmetry in Nonlinear Mathematical Physics, Vol. II, Kiev (2000), pp. 364–370.

    Google Scholar 

  5. J. Dixmier, C*-Algebras and Their Representations [Russian translation], Nauka, Moscow (1974).

    Google Scholar 

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Authors and Affiliations

  1. Shevchenko Kiev National University, Kiev

    S. V. Popovych

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    T. Yu. Maistrenko

Authors
  1. S. V. Popovych
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  2. T. Yu. Maistrenko
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Popovych, S.V., Maistrenko, T.Y. C*-Algebras Associated with \(F_{2^n }\) Unimodal Dynamical Systems. Ukrainian Mathematical Journal 53, 1106–1115 (2001). https://doi.org/10.1023/A:1013377115391

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  • DOI: https://doi.org/10.1023/A:1013377115391

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