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.*Proc. Steklov Inst. Math.***90**(1967). Transl. A. M. S. MR**0224110 (36:7157)****[A.Si]**D. V. Anosov and Ya. G. Sinai. Certain smooth ergodic systems.*Russ. Math. Surv.***22**No. 5 (1967), 103-167. MR**0224771 (37:370)****[B.1]**R. Bowen. Symbolic dynamics for hyperbolic flows.*Amer. J. Math.***95**(1973), 429-460. MR**0339281 (49:4041)****[B.2]**R. Bowen. The equidistribution of closed geodesics.*Amer. J. Math.***94**(1972), 413-423. MR**0315742 (47:4291)****[D]**D. Dolgopyat. On decay of correlations in Anosov flows.*Ann. of Math.***147**(1998), 357-390. MR**1626749 (99g:58073)****[F]**D. Fried. Meromorphic zeta functions for analytic flows.*Comm. Math. Phys.***174**(1995), 161-190. MR**1372805 (97a:58148)****[M]**G. Margulis. Certain measures associated with U-flows on compact manifolds.*Func. Anal. Appl.***4**(1969), 55-67. MR**0272984 (42:7865)****[P.P]**W. Parry and M. Pollicott. An analogue of the prime number theorem for closed orbits of Axiom A flows.*Ann. of Math.***118**(1983), 573-591. MR**0727704 (85i:58105)****[P.S]**M. Pollicott and R. Sharp. Exponential error terms for growth functions on negatively curved surfaces.*Amer. J. Math.***120**(1998), 1019-1042. MR**1646052 (99h:58148)****[Ra]**M. Ratner. Markov partitions for Anosov flows on -dimensional manifolds.*Israel J. Math.***15**(1973), 92-114. MR**0339282 (49:4042)****[R.1]**D. Ruelle.*Thermodynamic Formalism*. Addison Wesley, Reading, MA, 1978. MR**0511655 (80g:82017)****[R.2]**D. Ruelle.*Dynamical zeta functions for piecewise monotone maps of the interval*. CRM monograph series No. 4. A. M. S., 1994. MR**1274046 (95m:58101)****[Ru]**H. H. Rugh. The correlation spectrum for hyperbolic analytic maps.*Nonlinearity***5**(1992), 1237-1263. MR**1192517 (93i:58121)****[Se]**A. Selberg. Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series.*J. Indian Math. Soc.***20**(1956), 47-87. MR**0088511 (19:531g)****[Si.1]**Ya. G. Sinai. The asymptotic behaviour of the number of closed geodesics on a compact manifold of negative curvature.*Transl. A. M. S.***73**(1968), 227-250. MR**0229178 (37:4752)****[Si.2]**Ya. G. Sinai. The construction of Markov partitions.*Func. Anal. Appl.***2**(1968), 70-80. MR**0250352 (40:3591)****[Sm]**S. Smale. Differentiable dynamical systems.*Bull. A. M. S.***73**(1967), 747-817. MR**0228014 (37:3598)**

Review Information:

Reviewer: William Parry

Affiliation: University of Warwick

Email: b.parry@warwick.ac.uk

Journal: Bull. Amer. Math. Soc.

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

MSC (2000): Primary 37D20, 37D35

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.