Book Review

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Book Information:

Author: G. A. Margulis

Title: On some aspects of the theory of Anosov systems

Additional book information: Springer Monographs in Mathematics, Springer, Berlin, 2004, 138 pp., ISBN 3-540-40121-0, $69.95

**[A]**D. V. Anosov,*Geodesic flows on closed Riemannian manifolds of negative curvature*, Trudy Mat. Inst. Steklov.**90**(1967), 209 (Russian). MR**0224110****[A.Si]**D. V. Anosov and Ja. G. Sinaĭ,*Certain smooth ergodic systems*, Uspehi Mat. Nauk**22**(1967), no. 5 (137), 107–172 (Russian). MR**0224771****[B.1]**Rufus Bowen,*Symbolic dynamics for hyperbolic flows*, Amer. J. Math.**95**(1973), 429–460. MR**0339281****[B.2]**Rufus Bowen,*The equidistribution of closed geodesics*, Amer. J. Math.**94**(1972), 413–423. MR**0315742****[D]**Dmitry Dolgopyat,*On decay of correlations in Anosov flows*, Ann. of Math. (2)**147**(1998), no. 2, 357–390. MR**1626749**, 10.2307/121012**[F]**David Fried,*Meromorphic zeta functions for analytic flows*, Comm. Math. Phys.**174**(1995), no. 1, 161–190. MR**1372805****[M]**G. A. Margulis,*Certain measures that are connected with U-flows on compact manifolds*, Funkcional. Anal. i Priložen.**4**(1970), no. 1, 62–76 (Russian). MR**0272984****[P.P]**William Parry and Mark Pollicott,*An analogue of the prime number theorem for closed orbits of Axiom A flows*, Ann. of Math. (2)**118**(1983), no. 3, 573–591. MR**727704**, 10.2307/2006982**[P.S]**Mark Pollicott and Richard Sharp,*Exponential error terms for growth functions on negatively curved surfaces*, Amer. J. Math.**120**(1998), no. 5, 1019–1042. MR**1646052****[Ra]**M. Ratner,*Markov partitions for Anosov flows on 𝑛-dimensional manifolds*, Israel J. Math.**15**(1973), 92–114. MR**0339282****[R.1]**David Ruelle,*Thermodynamic formalism*, Encyclopedia of Mathematics and its Applications, vol. 5, Addison-Wesley Publishing Co., Reading, Mass., 1978. The mathematical structures of classical equilibrium statistical mechanics; With a foreword by Giovanni Gallavotti and Gian-Carlo Rota. MR**511655****[R.2]**David Ruelle,*Dynamical zeta functions for piecewise monotone maps of the interval*, CRM Monograph Series, vol. 4, American Mathematical Society, Providence, RI, 1994. MR**1274046****[Ru]**Hans H. Rugh,*The correlation spectrum for hyperbolic analytic maps*, Nonlinearity**5**(1992), no. 6, 1237–1263. MR**1192517****[Se]**A. Selberg,*Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series*, J. Indian Math. Soc. (N.S.)**20**(1956), 47–87. MR**0088511****[Si.1]**Ja. G. Sinaĭ,*Asymptotic behavior of closed geodesics on compact manifolds with negative curvature*, Izv. Akad. Nauk SSSR Ser. Mat.**30**(1966), 1275–1296 (Russian). MR**0229178****[Si.2]**Ja. G. Sinaĭ,*Construction of Markov partitionings*, Funkcional. Anal. i Priložen.**2**(1968), no. 3, 70–80 (Loose errata) (Russian). MR**0250352****[Sm]**S. Smale,*Differentiable dynamical systems*, Bull. Amer. Math. Soc.**73**(1967), 747–817. MR**0228014**, 10.1090/S0002-9904-1967-11798-1

Review Information:

Reviewer: William Parry

Affiliation: University of Warwick

Email: b.parry@warwick.ac.uk

Journal: Bull. Amer. Math. Soc.

**42**(2005), 257-261

Published electronically: February 10, 2005

Review copyright: © Copyright 2005 American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.