Preview

Doklady of the National Academy of Sciences of Belarus

Advanced search

Spectral potential of transfer operators and topological pressure

https://doi.org/10.29235/1561-8323-2022-66-6-567-573

Abstract

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.

About the Authors

V. I. Bakhtin
Belarusian State University
Belarus

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

4, Nezavisimosti Ave., 220030, Minsk



I. A. Ivanishko
Belarusian State University
Belarus

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

4, Nezavisimosti Ave., 220030, Minsk



A. V. Lebedev
Belarusian State University
Belarus

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

4, Nezavisimosti Ave., 220030, Minsk



References

1. Walters P. An introduction to ergodic theory. Graduate Texts in Mathematics, vol. 79. New York, Berlin, Springer-Verlag, 1982.

2. Bowen 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/bfb0081279

3. Ruelle D. Thermodynamic formalism. Encyclopedia of Math. and its Appl, Vol. 5, Reading, Mass. Addison-Wesley, 1978.

4. Walters 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/s0002-9947-1978-0466493-1

5. 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/bf01077431

6. Ruelle D. The thermodynamic formalism for expanding maps. Communications in Mathematical Physics, 1989, vol. 125, no. 2, pp. 239–262. https://doi.org/10.1007/bf01217908

7. 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).

8. Fan 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/s002200100538

9. Przytycki F., Urbanski M. Conformal Fractals: Ergodic Theory Methods, London Mathematical Society Lecture Note Series 371. Cambridge University Press, 2010. https://doi.org/10.1017/cbo9781139193184

10. Bardadyn 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


Review

Views: 280


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)