Nous caractérisons l’ensemble des périodes et la structure des applications de type Lorenz en fonction de l’intervalle de rotation. Pour ces applications nous donnons la meilleure borne inférieure de l’entropie topologique comme une fonction de l’intervalle de rotation
We characterize the set of periods and its structure for the Lorenz-like maps depending on the rotation interval. Also, for these maps we give the best lower bound of the topological entropy as a function of the rotation interval.
@article{AIF_1989__39_4_929_0, author = {Alsed\`a, Lluis and Llibre, J. and Misiurewicz, M. and Tresser, C.}, title = {Periods and entropy for Lorenz-like maps}, journal = {Annales de l'Institut Fourier}, volume = {39}, year = {1989}, pages = {929-952}, doi = {10.5802/aif.1195}, mrnumber = {91e:58146}, zbl = {0678.34047}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1989__39_4_929_0} }
Alsedà, Lluis; Llibre, J.; Misiurewicz, M.; Tresser, C. Periods and entropy for Lorenz-like maps. Annales de l'Institut Fourier, Tome 39 (1989) pp. 929-952. doi : 10.5802/aif.1195. http://gdmltest.u-ga.fr/item/AIF_1989__39_4_929_0/
[ALMM] Lower bounds for the topological entropy of continuous maps of the circle of degree one, Nonlinearity, 1 (1988), 463-479. | MR 89m:58119 | Zbl 0663.54023
, , and ,[ALMS] Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point, Ergod. Th. and Dynam. Sys., 5 (1985), 501-518. | MR 87h:58185 | Zbl 0592.54037
, , and ,[ALM] Periodic orbits of maps of Y, Trans. Amer. Math. Soc., 313 (1989), 475-538. | MR 90c:58145 | Zbl 0803.54032
, and ,[BGMY] Periodic points and topological entropy of one-dimensional maps, Springer, Lect. Notes in Math., 819 (1980), 18-39. | MR 82j:58097 | Zbl 0447.58028
, , and ,[CGT] Une remarque sur la structure des endomorphismes de degré 1 du cercle, C.R. Acad. Sc. Paris, 299, Sér. I (1984), 145-148. | MR 86b:58102 | Zbl 0584.58004
, and ,[GPTT] New universal scenarios for the onset of chaos in Lorenz type flows, Phys. Rev. Lett., 57 (1986), 925-928.
, , and ,[GT] Dynamique régulière ou chaotique. Applications du cercle ou de l'intervalle ayant une discontinuité, C.R. Acad. Sc., Paris, 300, Ser. I (1985), 311-313. | MR 86i:58085 | Zbl 0595.58031
and ,[G1] A strange, strange attractor, in the Hopf Bifurcation and its applications, Eds. J. E. Marsden and M. McCracken, Appl. Math. Sc. (Springer), 19 (1976), 368-381.
,[G2] Bifurcations of Dynamical Systems in : Dynamical Systems C.I.M.E. Lectures, Progress in Mathematics, 8, Birkhäuser, Boston, 1980. | MR 82g:58065 | Zbl 0451.58025
,[H1] The maximal measure for linear mod. one transformations, J. London Math. Soc., 23 (1981), 92-112. | MR 82c:28040 | Zbl 0431.54025
,[H2] Periodic points for piecewise monotonic transformation, Ergod. Th. and Dynam. Sys., 5 (1985), 237-256. | MR 87i:58141 | Zbl 0572.54036
,[L] Deterministic non-periodic flow, J. Atmos. Sci., 20 (1963), 130-141.
,[M1] Periodic points of maps of degree one of a circle, Ergod Th. and Dynam. Sys., 2 (1982), 221-227. | MR 84j:58101 | Zbl 0508.58038
,[M2] Twist sets for maps of a circle, Ergod. Th. and Dynam. Sys., 4 (1984), 391-404. | MR 86m:58135 | Zbl 0573.58019
,[M3] Rotation intervals for a class of maps of the real line into itself, Ergod. Th. and Dynam. Sys., 6 (1986), 117-132. | MR 87k:58131 | Zbl 0615.54030
,[MS] Entropy of piecewise monotone mappings, Studia Math., 67 (1980), 45-63. | MR 82a:58030 | Zbl 0445.54007
and ,[MT] On iterated maps of the interval, in Dynamical Systems, Ed. J. C. Alexander, Lecture Notes in Math., 1342 (1988), 465-563. | MR 90a:58083 | Zbl 0664.58015
and ,[P] The Lorenz attractor and a related population model, Lect. Notes in Math., Springer, 729 (1979), 169-187. | MR 81f:58027 | Zbl 0431.92022
,[R] Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar., 8 (1957), 477-493. | Zbl 0079.08901
,[RT] Rotation numbers for monotone functions on the circle, J. London Math. Soc., 34 (1986), 360-368. | MR 88b:58127 | Zbl 0623.58008
and ,