Mather measures and the Bowen–Series transformation

A. O. Lopes; Ph. Thieullen

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 5, page 663-682
  • ISSN: 0294-1449

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Lopes, A. O., and Thieullen, Ph.. "Mather measures and the Bowen–Series transformation." Annales de l'I.H.P. Analyse non linéaire 23.5 (2006): 663-682. <http://eudml.org/doc/78706>.

@article{Lopes2006,
author = {Lopes, A. O., Thieullen, Ph.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {stable norm; Mather measures; minimizing measures; Bowen-series transformations; geodesic billiard},
language = {eng},
number = {5},
pages = {663-682},
publisher = {Elsevier},
title = {Mather measures and the Bowen–Series transformation},
url = {http://eudml.org/doc/78706},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Lopes, A. O.
AU - Thieullen, Ph.
TI - Mather measures and the Bowen–Series transformation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 5
SP - 663
EP - 682
LA - eng
KW - stable norm; Mather measures; minimizing measures; Bowen-series transformations; geodesic billiard
UR - http://eudml.org/doc/78706
ER -

References

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  1. [1] Adler R., Flatto L., Geodesic flows, interval maps and symbolic dynamics, Bull. Amer. Math. Soc.25 (1991) 229-334. Zbl0802.58037MR1085823
  2. [2] Anantharaman N., Counting geodesics which are optimal in homology, Ergodic Theory Dynam. Systems23 (2) (2003) 353-388. Zbl1042.37048MR1972225
  3. [3] Bangert V., Mather sets for twist maps and geodesics on tori, Dynam. Report.I (1988) 1-56. Zbl0664.53021MR945963
  4. [4] Bangert V., Minimal geodesics, Ergodic Theory Dynam. Systems10 (1989) 263-286. Zbl0676.53055MR1062758
  5. [5] Bedford T., Keane M., Series C., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford Univ. Press, Oxford, 1991. Zbl0743.00040MR1130170
  6. [6] Bekka M., Mayer M., Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, Cambridge Univ. Press, Cambridge, 2000. Zbl0961.37001MR1781937
  7. [7] Bowen R., Series C., Markov maps associated to Fuchsian groups, Publ. Math. IHES50 (1979) 153-170. Zbl0439.30033MR556585
  8. [8] Carneiro M.J., On minimizing measures of the action of autonomous Lagrangians, Nonlinearity8 (6) (1995) 1077-1085. Zbl0845.58023MR1363400
  9. [9] G. Contreras, R. Iturriaga, Global minimizers for autonomous Lagrangians, in: 22 Coloq. Bras. Mat. 1999, IMPA, Rio de Janeiro, Brasil. Zbl0957.37065MR1720372
  10. [10] Contreras G., Delgado J., Iturriaga R., Lagrangian flows: the dynamics of globally minimizing orbits, Bol. Soc. Brassil. Mat.28 (2) (1997) 155-196. Zbl0892.58065MR1479500
  11. [11] Contreras G., Lopes A., Thieullen P., Lyapunov Minimizing Measures for expanding maps of the circle, Ergodic Theory Dynam. Systems21 (2001) 1379-1409. Zbl0997.37016MR1855838
  12. [12] R. Exel, A. Lopes, C * -Algebras, approximately proper equivalence relations, and thermodynamic formalism, Ergodic Theory Dynam. Systems (2003), in press. Zbl1065.46049MR2085390
  13. [13] Farkas H., Kra I., Riemann Surfaces, Springer-Verlag, 1980. Zbl0475.30001MR583745
  14. [14] Fathi A., Solutions KAM faibles conjuguees et barrieres de Peierls, C. R. Acad. Sci. Paris, Ser. I235 (1997) 649-652. Zbl0943.37031MR1473840
  15. [15] A. Fathi, Weak KAM Theorem in Lagrangian Dynamics, Lyons, 2000. 
  16. [16] Ford L., Automorphic Functions, Chelsea, 1972. JFM55.0810.04
  17. [17] Katok S., Fuchsian Groups, Univ. of Chicago Press, 1992. Zbl0753.30001MR1177168
  18. [18] Lopes A.O., Thieullen P., Subactions for Anosov diffeomorphisms, geometric methods in dynamics, in: Astérisque, Soc. Math. France, 2003, pp. 135-146. Zbl1045.37010MR2040005
  19. [19] Lopes A.O., Thieullen P., Subactions for Anosov Flows, Ergodic Theory Dynam. Systems25 (2) (2005) 605-628. Zbl1078.37021MR2129112
  20. [20] Mañé R., Generic properties and problems of minimizing measures of Lagrangian systems, Nonlinearity9 (2) (1996) 273-310. Zbl0886.58037MR1384478
  21. [21] D. Massart, Normes stables de surfaces, Thèse E.N.S. Lyon, 1996. MR1438388
  22. [22] Massart D., Stable norms of surfaces: local structure of the unit ball of rational directions, Geom. Funct. Anal.7 (6) (1997) 996-1010. Zbl0903.58001MR1487751
  23. [23] Mather J., Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z.207 (2) (1991) 169-207. Zbl0696.58027MR1109661
  24. [24] Paternain G., Geodesic Flows, Birkhäuser, 1999. Zbl0930.53001MR1712465
  25. [25] Series C., Geometrical Markov coding on surface of constant negative curvature, Ergodic Theory Dynam. Systems6 (1986) 601-625. Zbl0593.58033MR873435

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