Essential dynamics for Lorenz maps on the real line and the lexicographical world
Labarca, Rafael ; Moreira, Carlos Gustavo
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 683-694 / Harvested from Numdam
@article{AIHPC_2006__23_5_683_0,
     author = {Labarca, Rafael and Moreira, Carlos Gustavo},
     title = {Essential dynamics for Lorenz maps on the real line and the lexicographical world},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {23},
     year = {2006},
     pages = {683-694},
     doi = {10.1016/j.anihpc.2005.09.001},
     mrnumber = {2259612},
     zbl = {05072657},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_5_683_0}
}
Labarca, Rafael; Moreira, Carlos Gustavo. Essential dynamics for Lorenz maps on the real line and the lexicographical world. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 683-694. doi : 10.1016/j.anihpc.2005.09.001. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_5_683_0/

[1] Brucks K.M., Misiurewicz M., Tresser Ch., Monotonicity properties of the family of trapezoidals maps, Comm. Math. Phys. 137 (1991) 1-12. | MR 1099253 | Zbl 0721.58017

[2] Campbell D.K., Galeeva R., Tresser Ch., Uherka D.J., Piecewise linear models for the quasiperiodic transition to chaos, Chaos 6 (2) (1996) 121-154. | MR 1393554 | Zbl 1055.37532

[3] Furstenberg H., Disjointness in ergodic theory, Math. Systems Theory 1 (1969) 1-49. | MR 213508 | Zbl 0146.28502

[4] Galeeva R., Martens M., Tresser Ch., Inducing, slopes and conjugacy classes, Israel J. Math. 99 (1997) 123-147. | MR 1469090 | Zbl 0889.58031

[5] Gambaudo J.M., Tresser Ch., Dynamique régulière ou chaotique. Applications du cercle ou l'intervalle ayant une discontinuité, C. R. Acad. Soc. Paris, Sér. I 300 (10) (1985) 311-313. | MR 786907 | Zbl 0595.58031

[6] Glendinning P., Sparrow C., Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps, Physica D 62 (1993) 22-50. | MR 1207415 | Zbl 0783.58046

[7] Guckenheimer J., A strange, strange attractor, in: Marsden J.E., Mccracken M. (Eds.), Hopf Bifurcations and its Applications, Springer-Verlag, Berlin, 1976, pp. 368-381. | MR 494309

[8] Guckenheimer J., Williams R.F., Structural stability of Lorenz attractors, Publ. Math. IHES 50 (1979) 59-72. | Numdam | MR 556582 | Zbl 0436.58018

[9] Hubbard J.H., Sparrow C.T., The classification of topologically expansive Lorenz maps, Comm. Pure Appl. Math. XLIII (1990) 431-443. | MR 1047331 | Zbl 0714.58041

[10] R. Labarca, C.G. Moreira, Bifurcations of the essential dynamics of Lorenz maps and the application to Lorenz like flows: contributions to the study of the contracting case, Preprint, 2003.

[11] Labarca R., Moreira C.G., Bifurcations of the essential dynamics of Lorenz maps and the application to Lorenz like flows: contributions to the study of the expanding case, Bol. Soc. Bras. Mat. (N.S.) 32 (2) (2001) 107-144. | MR 1860864 | Zbl 0991.37017

[12] Labarca R., Moreira C.G., Bifurcation of the essential dynamics of Lorenz maps on the real line and the bifurcation scenario for the lineal family, Sci. Ser. A Math. Sci. (N.S.) 7 (2001) 13-29. | MR 1927206 | Zbl 05080598

[13] Lorenz E.N., Deterministic non-periodic flow, J. Atmos. Sci. 20 (1963) 130-141.

[14] Mackay R.S., Tresser Ch., Boundary of topological chaos for bimodal maps of the interval, J. London Math. Soc. (2) 37 (1988) 164-181. | MR 921755 | Zbl 0608.54016

[15] Mackay R.S., Tresser Ch., Some flesh on the skeleton: the bifurcation structure of bimodals maps, Physica D 27 (1987) 412-422. | MR 913688 | Zbl 0626.58038

[16] De Melo W., Van Strien S., One-Dimensional Dynamics, Springer-Verlag, 1993. | MR 1239171 | Zbl 0791.58003

[17] Misiurewicz M., Szlenk W., Entropy of piecewise monotone mappings, Studia Math. 67 (1) (1980) 45-63. | MR 579440 | Zbl 0445.54007

[18] C. Moreira, Geometric properties of the Markov and Lagrange spectra, Preprint IMPA, 2004.

[19] Otero-Espinar M.V., Tresser Ch., Global complexity and essential simplicity: a conjectural picture of the boundary of chaos for smooth endomorphisms of the interval, Physica D 39 (1989) 163-168. | MR 1028713 | Zbl 0696.58033

[20] Rand D., The topological classification of Lorenz attractors, Math. Proc. Cambridge Philos. Soc. 83 (3) (1978) 451-460. | MR 481632 | Zbl 0375.58015

[21] Rhodes F., Kneading of Lorenz type for intervals and product spaces, Math. Proc. Cambridge Philos. Soc. 89 (1) (1981) 167-179. | MR 591983 | Zbl 0456.58017

[22] Ringland J., Tresser Ch., A genealogy for finite kneading sequences of bimodal maps on the interval, TAMS 347 (12) (1995) 4599-4624. | MR 1311914 | Zbl 0849.54033

[23] Tresser Ch., Nouveaux types de transitions vers une entropie topologique positive, C. R. Acad. Paris, Sér. I 296 (1983) 729-732. | MR 706669 | Zbl 0528.58032

[24] Tresser Ch., Williams R.F., Splitting words and Lorenz braids, Physica D 62 (1993) 15-21. | MR 1207414 | Zbl 0783.58041

[25] Urbański M., On Hausdorff dimension of invariant sets for expanding maps of a circle, Ergodic Theory Dynam. Systems 6 (1986) 295-309. | MR 857203 | Zbl 0631.58019

[26] Williams R.F., The structure of Lorenz attractors, in: Bernard P., Ratiu T. (Eds.), Turbulence Seminar Berkeley 1976/1977, Springer-Verlag, New York, 1977, pp. 94-112. | MR 461581