Essential dynamics for Lorenz maps on the real line and the lexicographical world

Rafael Labarca; Carlos Gustavo Moreira

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

  • Volume: 23, Issue: 5, page 683-694
  • ISSN: 0294-1449

How to cite

top

Labarca, Rafael, and 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 23.5 (2006): 683-694. <http://eudml.org/doc/78707>.

@article{Labarca2006,
author = {Labarca, Rafael, Moreira, Carlos Gustavo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {essential dynamics; lexicographical world; Hausdorff dimension; entropy},
language = {eng},
number = {5},
pages = {683-694},
publisher = {Elsevier},
title = {Essential dynamics for Lorenz maps on the real line and the lexicographical world},
url = {http://eudml.org/doc/78707},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Labarca, Rafael
AU - Moreira, Carlos Gustavo
TI - Essential dynamics for Lorenz maps on the real line and the lexicographical world
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 5
SP - 683
EP - 694
LA - eng
KW - essential dynamics; lexicographical world; Hausdorff dimension; entropy
UR - http://eudml.org/doc/78707
ER -

References

top
  1. [1] Brucks K.M., Misiurewicz M., Tresser Ch., Monotonicity properties of the family of trapezoidals maps, Comm. Math. Phys.137 (1991) 1-12. Zbl0721.58017MR1099253
  2. [2] Campbell D.K., Galeeva R., Tresser Ch., Uherka D.J., Piecewise linear models for the quasiperiodic transition to chaos, Chaos6 (2) (1996) 121-154. Zbl1055.37532MR1393554
  3. [3] Furstenberg H., Disjointness in ergodic theory, Math. Systems Theory1 (1969) 1-49. Zbl0146.28502MR213508
  4. [4] Galeeva R., Martens M., Tresser Ch., Inducing, slopes and conjugacy classes, Israel J. Math.99 (1997) 123-147. Zbl0889.58031MR1469090
  5. [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. I300 (10) (1985) 311-313. Zbl0595.58031MR786907
  6. [6] Glendinning P., Sparrow C., Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps, Physica D62 (1993) 22-50. Zbl0783.58046MR1207415
  7. [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. MR494309
  8. [8] Guckenheimer J., Williams R.F., Structural stability of Lorenz attractors, Publ. Math. IHES50 (1979) 59-72. Zbl0436.58018MR556582
  9. [9] Hubbard J.H., Sparrow C.T., The classification of topologically expansive Lorenz maps, Comm. Pure Appl. Math.XLIII (1990) 431-443. Zbl0714.58041MR1047331
  10. [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. Zbl0991.37017
  11. [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. Zbl0991.37017MR1860864
  12. [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. Zbl1160.37355MR1927206
  13. [13] Lorenz E.N., Deterministic non-periodic flow, J. Atmos. Sci.20 (1963) 130-141. 
  14. [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. Zbl0608.54016MR921755
  15. [15] MacKay R.S., Tresser Ch., Some flesh on the skeleton: the bifurcation structure of bimodals maps, Physica D27 (1987) 412-422. Zbl0626.58038MR913688
  16. [16] de Melo W., Van Strien S., One-Dimensional Dynamics, Springer-Verlag, 1993. Zbl0791.58003MR1239171
  17. [17] Misiurewicz M., Szlenk W., Entropy of piecewise monotone mappings, Studia Math.67 (1) (1980) 45-63. Zbl0445.54007MR579440
  18. [18] C. Moreira, Geometric properties of the Markov and Lagrange spectra, Preprint IMPA, 2004. 
  19. [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 D39 (1989) 163-168. Zbl0696.58033MR1028713
  20. [20] Rand D., The topological classification of Lorenz attractors, Math. Proc. Cambridge Philos. Soc.83 (3) (1978) 451-460. Zbl0375.58015MR481632
  21. [21] Rhodes F., Kneading of Lorenz type for intervals and product spaces, Math. Proc. Cambridge Philos. Soc.89 (1) (1981) 167-179. Zbl0456.58017MR591983
  22. [22] Ringland J., Tresser Ch., A genealogy for finite kneading sequences of bimodal maps on the interval, TAMS347 (12) (1995) 4599-4624. Zbl0849.54033MR1311914
  23. [23] Tresser Ch., Nouveaux types de transitions vers une entropie topologique positive, C. R. Acad. Paris, Sér. I296 (1983) 729-732. Zbl0528.58032MR706669
  24. [24] Tresser Ch., Williams R.F., Splitting words and Lorenz braids, Physica D62 (1993) 15-21. Zbl0783.58041MR1207414
  25. [25] Urbański M., On Hausdorff dimension of invariant sets for expanding maps of a circle, Ergodic Theory Dynam. Systems6 (1986) 295-309. Zbl0631.58019MR857203
  26. [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. MR461581

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.