Closed geodesics in homology classes on surfaces of variable negative curvature
Steven P. Lalley
Source: Duke Math. J. Volume 58, Number 3 (1989), 795-821.
First Page PDF: View first page of article (PDF, 91 KB)Primary Subjects: 58F17
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077307679
Mathematical Reviews number (MathSciNet):
MR1016446
Zentralblatt MATH identifier:
0732.53035
Digital Object Identifier: doi:10.1215/S0012-7094-89-05837-7
References
[1] L. M. Abramov, On the entropy of a flow, Dokl. Akad. Nauk SSSR 128 (1959), 873–875.
Mathematical Reviews (MathSciNet):
MR22:4816
Zentralblatt MATH:
0094.10002
[2] R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York, 1964.
Mathematical Reviews (MathSciNet):
MR29:6401
Zentralblatt MATH:
0132.16003
[3] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429–460.
Mathematical Reviews (MathSciNet):
MR49:4041
Zentralblatt MATH:
0282.58009
Digital Object Identifier: doi:10.2307/2373793
JSTOR: links.jstor.org
[4] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Springer-Verlag, Berlin, 1975.
Mathematical Reviews (MathSciNet):
MR56:1364
Zentralblatt MATH:
0308.28010
[5] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), no. 3, 181–202.
Mathematical Reviews (MathSciNet):
MR52:1786
Zentralblatt MATH:
0311.58010
Digital Object Identifier: doi:10.1007/BF01389848
[6] A. Katsuda and T. Sunada, Homology and closed geodesics in a compact Riemann surface, Amer. J. Math. 110 (1988), no. 1, 145–155.
Mathematical Reviews (MathSciNet):
MR89e:58093
Zentralblatt MATH:
0647.53036
Digital Object Identifier: doi:10.2307/2374542
JSTOR: links.jstor.org
[7] S. P. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. in Appl. Math. 8 (1987), no. 2, 154–193.
Mathematical Reviews (MathSciNet):
MR89e:58088
Zentralblatt MATH:
0637.58013
Digital Object Identifier: doi:10.1016/0196-8858(87)90012-1
[8] S. P. Lalley, Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations, and their fractal limits, preprint, 1987.
Mathematical Reviews (MathSciNet):
MR886923
Digital Object Identifier: doi:10.1016/0196-8858(87)90012-1
[9] G. A. Margulis, Applications of ergodic theory to the investigation of manifolds of negative curvature, Functional Anal. Appl. 3 (1969), 335–336.
Zentralblatt MATH:
0207.20305
Mathematical Reviews (MathSciNet):
MR257933
[10] W. Parry, Bowen's equidistribution theory and the Dirichlet density theorem, Ergodic Th. Dynamical Systems 4 (1984), 135–146.
Mathematical Reviews (MathSciNet):
MR758898
Digital Object Identifier: doi:10.1017/S0143385700002315
[11] W. Parry and M. 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.
Mathematical Reviews (MathSciNet):
MR85i:58105
Zentralblatt MATH:
0537.58038
Digital Object Identifier: doi:10.2307/2006982
JSTOR: links.jstor.org
[12] R. Phillips and P. Sarnak, Geodesics in homology classes, Duke Math. J. 55 (1987), no. 2, 287–297.
Mathematical Reviews (MathSciNet):
MR88g:58151
Zentralblatt MATH:
0642.53050
Digital Object Identifier: doi:10.1215/S0012-7094-87-05515-3
Project Euclid: euclid.dmj/1077306021
[13] M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math. 81 (1985), no. 3, 413–426.
Mathematical Reviews (MathSciNet):
MR87i:58148
Zentralblatt MATH:
0591.58025
Digital Object Identifier: doi:10.1007/BF01388579
[14] M. Pollicott, Meromorphic extensions of generalised zeta functions, Invent. Math. 85 (1986), no. 1, 147–164.
Mathematical Reviews (MathSciNet):
MR87k:58218
Zentralblatt MATH:
0604.58042
Digital Object Identifier: doi:10.1007/BF01388795
[15] M. Pollicott, A complex Ruelle-Perron-Frobenius theorem and two counterexamples, Ergodic Theory Dynam. Systems 4 (1984), no. 1, 135–146.
Mathematical Reviews (MathSciNet):
MR88i:58097
Zentralblatt MATH:
0575.47009
Digital Object Identifier: doi:10.1017/S0143385700002327
[16] M. Pollicott, to appear in J. Diff. Geom.
[17] M. Ratner, Markov partitions for Anosov flows on $n$-dimensional manifolds, Israel J. Math. 15 (1973), 92–114.
Mathematical Reviews (MathSciNet):
MR49:4042
Zentralblatt MATH:
0269.58010
Digital Object Identifier: doi:10.1007/BF02771776
[18] D. Ruelle, Statistical mechanics of a one-dimensional lattice gas, Comm. Math. Phys. 9 (1968), 267–278.
Mathematical Reviews (MathSciNet):
MR38:3013
Zentralblatt MATH:
0165.29102
Digital Object Identifier: doi:10.1007/BF01654281
Project Euclid: euclid.cmp/1103840801
[19] D. Ruelle, Thermodynamic formalism, Encyclopedia of Mathematics and its Applications, vol. 5, Addison-Wesley Publishing Co., Reading, Mass., 1978.
Mathematical Reviews (MathSciNet):
MR80g:82017
Zentralblatt MATH:
0401.28016
Duke Mathematical Journal