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Book Review

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Book Information

Author(s): G. A. Margulis; with a survey, ``Periodic orbits of hyperbolic flows'', by Richard Sharp
Title: On some aspects of the theory of Anosov systems
Additional book information: Springer Monographs in Mathematics, Springer, Berlin, 2004, 138, $69.95, 3-540-40121-0

References:

[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 $n$-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)

Additional Information:

Reviewer(s):
William Parry
Affiliation: University of Warwick
Email: b.parry@warwick.ac.uk

Review Information:
Journal: Bull. Amer. Math. Soc. 42 (2005), 257-261.

MSC (2000): Primary 37D20, 37D35
DOI: 10.1090/S0273-0979-05-01051-7
PII: S 0273-0979(05)01051-7
Posted: February 10, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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