This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Ya. G. Sinai, "Dynamical systems with elastic reflections. Ergodic properties of dispersed billiards," Usp. Mat. Nauk,25, No. 2, 141–192 (1970).
L. A. Bunimovich and Ya. G. Sinai, "The basic theorem of the theory of dispersed billiards," Mat. Sb.,90, No. 3, 415–431 (1973).
L. A. Bunimovich, "Nearly dispersed billiards," Mat. Sb.,95, No. 1, 49–73 (1974).
L. A. Bunimovich, "On the ergodic properties of nowhere dispersing billiards," Commun. Math. Phys.,65, No. 3, 295–312 (1979).
L. A. Bunimovich, Ya. G. Sinai, and N. I. Chernov, "Markov partitions for two-dimensional hyperbolic billiards," Usp. Mat. Nauk,45, No. 3, 97–134 (1990).
Dynamical Systems, Vol. 2, Itogi Nauki i Tekhniki. Ser. Sov. Probl. Mat. Fundam. Napravl. (1985).
A. Katok and J. M. Strelcyn, Smooth Maps with Singularities: Invariant Manifolds, Entropy and Billiards, Lect. Notes Math.,1222 (1987).
V. M. Alekseev and M. V. Yakobson, "Symbolic dynamics and hyperbolic dynamical systems," in: R. Bowen, Methods of Symbolic Dynamics [Russian translation], Mir, Moscow (1979), pp. 196–240.
R. Bowen, "Topological entropy for noncompact sets," Trans. Am. Math. Soc.,184, 125–136 (1973).
Ya. B. Pesin and B. S. Pitskel’, "Topological pressure and a variational principle for noncompact sets," Funkts. Anal. Prilozhen.,18, No. 4, 50–63 (1984).
B. M. Gurevich, "Topological entropy of a countable Markov chain," Dokl. Akad. Nauk SSSR,187, No. 4, 715–718 (1969).
I. Salama, "Topological entropy and recurrence of countable chains," Pac. J. Math.,132, No. 2, 325–341 (1988).
L. Stojanov, "An estimate from above of the number of periodic orbits for semi-dispersed billiards," Commun. Math. Phys.,124, No. 2, 217–227 (1989).
A. Katok, "Lyapunov exponents, entropy and periodic orbits of diffeomorphisms," Publ. Math. IHES,51, 137–173 (1980).
M. Ikawa, "Decay of solutions of the wave equation in the exterior of several convex bodies," Ann. Inst. Fourier,38, 113–146 (1988).
T. Morita, "The symbolic representation of billiards without boundary condition," Preprint, Tokyo Inst. Technol., Tokyo (1989).
N. I. Chernov, V. K. Fedyanin, and V. A. Shvedovsky, "Calculation of the billiards hentropy in the closed plane region with the scattering boundary," Preprint E17-83-236, JINR, Dubna (1983).
A. Katok, "The growth rate for the number of singular and periodic orbits for a polygonal billiard," Commun. Math. Phys.,111, No. 1, 151–160 (1987).
Joint Institute of Nuclear Research. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 1, pp. 50–57, January–March, 1991.
About this article
Cite this article
Chernov, N.I. Topological entropy and periodic points of two-dimensional hyperbolic billiards. Funct Anal Its Appl 25, 39–45 (1991). https://doi.org/10.1007/BF01090675
- Functional Analysis
- Periodic Point
- Topological Entropy
- Hyperbolic Billiard