t-Entropy formulae for concrete classes of transfer operators

Authors

  • Krzysztof Bardadyn University of Bialystok, 1M K. Ciolkowskiego Street, Bialystok 15-245, Poland
  • Bartosz Kosma Kwasniewski University of Bialystok, 1M K. Ciolkowskiego Street, Bialystok 15-245, Poland
  • Kirill S. Kurnosenko Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Andrei V. Lebedev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0002-8251-6048 (unauthenticated)

Keywords:

transfer operator, spectral potential, t-entropy, invariant measure, metric entropy

Abstract

t-Entropy is a principal object of the spectral theory of operators, generated by dynamical systems, namely, weighted shift operators and transfer operators. In essence t-entropy is the Fenchel – Legendre transform of the spectral potential of an operator in question and derivation of explicit formulae for its calculation is a rather nontrivial problem. In the article explicit formulae for t-entropy for two the most exploited in applications classes of transfer operators are obtained. Namely, we consider transfer operators generated by reversible mappings (i. e. weighted shift operators) and transfer operators generated by local homeomorphisms (i. e. Perron – Frobenius operators). In the first case t-entropy is computed by means of integrals with respect to invariant measures, while in the second case it is computed in terms of integrals with respect to invariant measures and Kolmogorov – Sinai entropy.

Author Biographies

  • Krzysztof Bardadyn, University of Bialystok, 1M K. Ciolkowskiego Street, Bialystok 15-245, Poland

    assistant at the department of analysis, faculty of mathematics

  • Bartosz Kosma Kwasniewski, University of Bialystok, 1M K. Ciolkowskiego Street, Bialystok 15-245, Poland

    doctor of science (mathematics); head of the department of analysis, faculty of mathematics

  • Kirill S. Kurnosenko, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    postgraduate student at the department of functional analysis and analytic economy, faculty of mechanics and mathematics

  • Andrei V. Lebedev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    doctor of science (physics and mathematics), full professor; head of the department of functional analysis and analytic economy, faculty of mechanics and mathematics

References

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Published

2019-11-28

Issue

No. 3 (2019): Journal of the Belarusian State University. Mathematics and Informatics

Section

Short Communications

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How to Cite

t-Entropy formulae for concrete classes of transfer operators. (2019). Journal of the Belarusian State University. Mathematics and Informatics, 3, 122-128. https://doi.org/10.33581/2520-6508-2019-3-122-128