Lyapunov minimizing measures for expanding maps of the circle

Ergodic Theory and Dynamical Systems

Volumn 21, Issue 5, 2001, Pages 1379-1409

  Contreras, G ^a   Lopes, A O ^b   Thieullen, Ph ^c  

^a CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS   (Mexico)

^b FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^c Université de Paris Sud   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040971816     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385701001663     Document Type: Article

References (24)

1. G. Atkinson. Recurrence of cocycles and random walks. J. London Math. Soc. 13(2) (1976), 486-488.
2. Th. Bousch. Le poisson n'a pas d'arêtes. Ann. Inst. Henri Poincaré 36 (2000), 489-508.
3. R. Bowen. Entropy for maps of the interval. J. Topology 16 (1977), 465-467.
4. M. Craizer. MSc Thesis, IMPA.
5. M. J. Dias-Carneiro. On minimizing measures of the action of autonomous Lagrangians. Nonlinearity 8 (1995), 1077-1085.
6. G. Contreras, J. Delgado and R. Iturriaga. Lagrangian flows: the dynamics of globally minimizing orbits - II. Bol. Soc. Bras. Mat. 28(2), (1997), 155-196.
7. G. Contreras, R. Iturriaga, G. P. Paternain and M. Paternain. Lagrangian graphs, minimizing measures and Mañé's critical values. Geom. Funct. Anal. 8(2) (1998), 417-444.
8. A. Fathi. Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Acad. Sci. Paris, I. 324 (1997), 1043-1046.
9. G. Forni and J. Mather. Action Minimizing Orbits in Hamiltonian Systems (Lecture Notes in Mathematics, 1589). Springer, 1994, pp. 92-186.
10. C. Grillenberger. Constructions of strictly ergodic systems I. Given entropy. Z. Wahrsch. Verw. Gebiete 25 (1973), 323-334.
11. C. Grillenberger. Constructions of strictly ergodic systems II. K-systems. Z. Wahrsch. Verw. Gebiete 25 (1973), 335-342.
12. B. R. Hunt. Maximal local Lyapunov dimension bounds the box dimension of chaotic attractors. Nonlinearity 9 (1996), 845-852.
13. Y. Guocheng and B. R. Hunt. Optimal orbits of hyperbolic systems. Preprint.
14. O. M. Jenkinson. Frequency-locking on the boundary of the barycenter set. Exp. Math. 9 (2000), 309-317.
15. O. M. Jenkinson. On the barycentre of invariant measures for circle maps. Preprint.
16. A. Lopes. Dimension spectra and a mathematical model for phase transitions. Adv. Appl. Math. 11(4) (1990), 475-502.
17. R. Mañe. The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces. Bol. Soc. Bras. Mat. 20(2) (1990), 1-24.
18. R. Mañe. Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity 9 (1996), 273-310.
19. R. Mañé. Lagrangian flows: the dynamics of globally minimizing orbits. Int. Congress on Dyn. Sys. in Montevideo (a tribute to Ricardo Mañé) (Pitman Research Notes in Mathematics, 362). Eds F. Ledrappier, J. L. Lewowicz and S. Newhouse. Longman, Harlow, 1996, pp. 120-131. Reprinted in Bol. Soc. Bras. Mat. 28(2) ( 1995), 141-153.
20. R. Mañé. Lagrangian flows: the dynamics of globally minimizing orbits. Int. Congress on Dyn. Sys. in Montevideo (a tribute to Ricardo Mañé) (Pitman Research Notes in Mathematics, 362). Eds F. Ledrappier, J. L. Lewowicz and S. Newhouse. Longman, Harlow, 1996, pp. 120-131. Reprinted in Bol. Soc. Bras. Mat. 28(2) ( 1995), 141-153.
21. W. Parry and M. Pollicott. Zeta function and the periodic orbit structure of hyperbolic dynamics. Asterisque 187-188, 1990.
22. R. Rockafellar. Convex Analysis. Princeton University Press, 1970.
23. Ph. Thieullen. Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems. J. Dynam. Diff. Eqn. 4(1) (1992), 127-159
24. A. Loyes and Ph. Thieullen. Sub-actions for Anosov diffeomorphisms. Preprint.