Mather measures and the Bowen-Series transformation
Lopes, A. O. ; Thieullen, Ph.
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 663-682 / Harvested from Numdam
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@article{AIHPC_2006__23_5_663_0,
     author = {Lopes, A. O. and Thieullen, Ph.},
     title = {Mather measures and the Bowen-Series transformation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {663-682},
     doi = {10.1016/j.anihpc.2004.12.005},
     zbl = {05072656},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_5_663_0}
}

Lopes, A. O.; Thieullen, Ph. Mather measures and the Bowen-Series transformation. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 663-682. doi : 10.1016/j.anihpc.2004.12.005. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_5_663_0/

[1] Adler R., Flatto L., Geodesic flows, interval maps and symbolic dynamics, Bull. Amer. Math. Soc. 25 (1991) 229-334. | MR 1085823 | Zbl 0802.58037

[2] Anantharaman N., Counting geodesics which are optimal in homology, Ergodic Theory Dynam. Systems 23 (2) (2003) 353-388. | MR 1972225 | Zbl 1042.37048

[3] Bangert V., Mather sets for twist maps and geodesics on tori, Dynam. Report. I (1988) 1-56. | MR 945963 | Zbl 0664.53021

[4] Bangert V., Minimal geodesics, Ergodic Theory Dynam. Systems 10 (1989) 263-286. | MR 1062758 | Zbl 0676.53055

[5] Bedford T., Keane M., Series C., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford Univ. Press, Oxford, 1991. | MR 1130170 | Zbl 0743.00040

[6] Bekka M., Mayer M., Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, Cambridge Univ. Press, Cambridge, 2000. | MR 1781937 | Zbl 0961.37001

[7] Bowen R., Series C., Markov maps associated to Fuchsian groups, Publ. Math. IHES 50 (1979) 153-170. | Numdam | MR 556585 | Zbl 0439.30033

[8] Carneiro M.J., On minimizing measures of the action of autonomous Lagrangians, Nonlinearity 8 (6) (1995) 1077-1085. | MR 1363400 | Zbl 0845.58023

[9] G. Contreras, R. Iturriaga, Global minimizers for autonomous Lagrangians, in: 22 Coloq. Bras. Mat. 1999, IMPA, Rio de Janeiro, Brasil. | MR 1720372 | Zbl 0957.37065

[10] Contreras G., Delgado J., Iturriaga R., Lagrangian flows: the dynamics of globally minimizing orbits, Bol. Soc. Brassil. Mat. 28 (2) (1997) 155-196. | MR 1479500 | Zbl 0892.58065

[11] Contreras G., Lopes A., Thieullen P., Lyapunov Minimizing Measures for expanding maps of the circle, Ergodic Theory Dynam. Systems 21 (2001) 1379-1409. | MR 1855838 | Zbl 0997.37016

[12] R. Exel, A. Lopes, C * -Algebras, approximately proper equivalence relations, and thermodynamic formalism, Ergodic Theory Dynam. Systems (2003), in press. | MR 2085390 | Zbl 1065.46049

[13] Farkas H., Kra I., Riemann Surfaces, Springer-Verlag, 1980. | MR 583745 | Zbl 0475.30001

[14] Fathi A., Solutions KAM faibles conjuguees et barrieres de Peierls, C. R. Acad. Sci. Paris, Ser. I 235 (1997) 649-652. | MR 1473840 | Zbl 0943.37031

[15] A. Fathi, Weak KAM Theorem in Lagrangian Dynamics, Lyons, 2000.

[16] Ford L., Automorphic Functions, Chelsea, 1972. | JFM 55.0810.04

[17] Katok S., Fuchsian Groups, Univ. of Chicago Press, 1992. | MR 1177168 | Zbl 0753.30001

[18] Lopes A.O., Thieullen P., Subactions for Anosov diffeomorphisms, geometric methods in dynamics, in: Astérisque, Soc. Math. France, 2003, pp. 135-146. | MR 2040005 | Zbl 1045.37010

[19] Lopes A.O., Thieullen P., Subactions for Anosov Flows, Ergodic Theory Dynam. Systems 25 (2) (2005) 605-628. | MR 2129112 | Zbl 1078.37021

[20] Mañé R., Generic properties and problems of minimizing measures of Lagrangian systems, Nonlinearity 9 (2) (1996) 273-310. | MR 1384478 | Zbl 0886.58037

[21] D. Massart, Normes stables de surfaces, Thèse E.N.S. Lyon, 1996. | MR 1438388

[22] Massart D., Stable norms of surfaces: local structure of the unit ball of rational directions, Geom. Funct. Anal. 7 (6) (1997) 996-1010. | MR 1487751 | Zbl 0903.58001

[23] Mather J., Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (2) (1991) 169-207. | MR 1109661 | Zbl 0696.58027

[24] Paternain G., Geodesic Flows, Birkhäuser, 1999. | MR 1712465 | Zbl 0930.53001

[25] Series C., Geometrical Markov coding on surface of constant negative curvature, Ergodic Theory Dynam. Systems 6 (1986) 601-625. | MR 873435 | Zbl 0593.58033