danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2022-66-6-567-573dan-1096Research ArticleМАТЕМАТИКАMATHEMATICSСпектральный потенциал трансфер-операторов и топологическое давлениеSpectral potential of transfer operators and topological pressureБахтинВ. И.BakhtinV. I.

Бахтин Виктор Иванович – доктор физико-математических наук, профессор.

пр. Независимости, 4, 220030, Минск

Victor I. Bakhtin – D. Sc. (Physics and Mathematics), Professor, Belarusian State University.

4, Nezavisimosti Ave., 220030, Minsk

bakhtin@tut.byИванишкоИ. А.IvanishkoI. A.

Иванишко Ия Александровна – кандидат физико-математических наук, старший преподаватель.

пр. Независимости, 4, 220030, Минск

Iya A. Ivanishko – Ph. D. (Physics and Mathematics), Senior Lecturer, Belarusian State University.

4, Nezavisimosti Ave., 220030, Minsk

iya.ivanishko@gmail.comЛебедевА. В.LebedevA. V.

Лебедев Андрей Владимирович – доктор физико-математических наук, профессор, заведующий кафедрой.

пр. Независимости, 4, 220030, Минск

Andrei V. Lebedev – D. Sc. (Physics and Mathematics), Professor, Head of the Department, Belarusian State University.

4, Nezavisimosti Ave., 220030, Minsk

lebedev@bsu.byБелорусский государственный университетBelarusian State University202203012023666567573Copyright © Бахтин В.И., Иванишко И.А., Лебедев А.В., 20232023Бахтин В.И., Иванишко И.А., Лебедев А.В.Bakhtin V.I., Ivanishko I.A., Lebedev A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/1096

Описаны взаимосвязи между спектральным радиусом трансфер-операторов и топологическим давлением для конечнолистных накрытий. Связи описываются с использованием новых динамических характеристик – разветвленности и форвард-энтропии. В общей ситуации эти характеристики позволяют выписать оценки для упомянутых объектов, которые переходят в равенства для несжимающих отображений.

The article describes the relations between spectral radius of transfer operators and topological pressure. The key role is played by new dynamical characteristics – rami-rate and forward entropy.

спектральный потенциалтопологическое давлениетопологическая энтропияразветвленностьфорвард-энтропияspectral potentialtopological pressuretopological entropyrami-rateforward entropyReferencesWalters, P. An introduction to ergodic theory / P. Walters // Graduate Texts in Mathematics. – New York; Berlin: Springer-Verlag, 1982. – Vol. 79.Walters P. An introduction to ergodic theory. Graduate Texts in Mathematics, vol. 79. New York, Berlin, Springer-Verlag, 1982.Bowen, R. Equilibrium states and the ergodic theory of Anosov diffeomorphisms / R. Bowen // Lecture Notes in Mathematics. – Berlin, Heidelberg, New York: Springer, 1975. – Vol. 470. https://doi.org/10.1007/bfb0081279Bowen R. Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lecture Notes in Mathematics, vol. 470. Berlin, Heidelberg, New York, Springer, 1975. https://doi.org/10.1007/bfb0081279Ruelle, D. Thermodynamic formalism / D. Ruelle // Encyclopedia of Math. and its Appl, Reading, Mass. – Addison-Wesley, 1978. – Vol. 5.Ruelle D. Thermodynamic formalism. Encyclopedia of Math. and its Appl, Vol. 5, Reading, Mass. Addison-Wesley, 1978.Walters, P. Invariant measures and equilibrium states for some mappings which expand distances / P. Walters // Trans. Am. Math. Soc. – 1978. – Vol. 236. – P. 121–153. https://doi.org/10.1090/s0002-9947-1978-0466493-1Walters P. Invariant measures and equilibrium states for some mappings which expand distances. Transactions of the American Mathematical Society, 1978, vol. 236, pp. 121–153. https://doi.org/10.1090/s0002-9947-1978-0466493-1Латушкин, Ю. Д. Операторы взвешенного сдвига на топологической марковской цепи / Ю. Д. Латушкин, А. М. Степин // Функц. анализ и его приложения. – 1988. – Т. 22, № 4. – С. 86–87.Latushkin Yu. D., Stepin A. M. Weighted shift operators on a topological Markov chain. Functional Analysis and Its Applications, 1988, vol. 22, no. 4, pp. 330–331. https://doi.org/10.1007/bf01077431Ruelle, D. The thermodynamic formalism for expanding maps / D. Ruelle // Comm. Math. Phys. – 1989. – Vol. 125, N 2. – P. 239–262. https://doi.org/10.1007/bf01217908Ruelle D. The thermodynamic formalism for expanding maps. Communications in Mathematical Physics, 1989, vol. 125, no. 2, pp. 239–262. https://doi.org/10.1007/bf01217908Лебедев, A. Спектральный радиус оператора взвешенного сдвига, вариационные принципы и топологическое давление / A. Лебедев, O. Маслак // Spectral and evolutionary problems. Proceedings of the Eighth Crimean Autumn Mathematical School Symposium (Simferopol, 1998). – Moscow, 1998. – P. 26–34.Lebedev A., Maslak O. Spectral radius of weighted shift operator, variational principles and topological pressure. Spectral and evolutionary problems. Proceedings of the Eighth Crimean Autumn Mathematical School Symposium (Simferopol, 1998). Moscow, 1998, pp. 26–34 (in Russian).Fan, A. H. On Ruelle–Perron–Frobenius Operators. I. Ruelle’s Theorem / A. H. Fan, Y. P. Jiang // Commun. Math. Phys. – 2001. – Vol. 223, N 1. – P. 125–141. https://doi.org/10.1007/s002200100538Fan A. H., Jiang Y. P. On Ruelle–Perron–Frobenius Operators. I. Ruelle Theorem. Communications in Mathematical Physics, 2001, vol. 223, no. 1, pp. 125–141. https://doi.org/10.1007/s002200100538Przytycki, F. Conformal Fractals: Ergodic Theory Methods, London Mathematical Society Lecture Note Series 371 / F. Przytycki, M. Urbanski. – Cambridge University Press, 2010. https://doi.org/10.1017/cbo9781139193184Przytycki F., Urbanski M. Conformal Fractals: Ergodic Theory Methods, London Mathematical Society Lecture Note Series 371. Cambridge University Press, 2010. https://doi.org/10.1017/cbo9781139193184Bardadyn, K. Spectrum of weighted isometries: C*-algebras, transfer operators and topological pressure / K. Bardadyn, B. K. Kwasniewski // Israel J. Math. – 2021. – Vol. 246, N 1. – P. 149–210. https://doi.org/10.1007/s11856-021-2246-6Bardadyn K., Kwasniewski B. K. Spectrum of weighted isometries: C*-algebras, transfer operators and topological pressure. Israel Journal of Mathematics, 2021, vol. 246, no. 1, pp. 149–210. https://doi.org/10.1007/s11856-021-2246-6

The authors declare that there are no conflicts of interest present.