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}, pages = {929--952}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {39}, number = {4}, year = {1989}, doi = {10.5802/aif.1195}, zbl = {0678.34047}, mrnumber = {91e:58146}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1195/} }
TY - JOUR AU - Alsedà, Lluis AU - Llibre, J. AU - Misiurewicz, M. AU - Tresser, C. TI - Periods and entropy for Lorenz-like maps JO - Annales de l'Institut Fourier PY - 1989 SP - 929 EP - 952 VL - 39 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1195/ DO - 10.5802/aif.1195 LA - en ID - AIF_1989__39_4_929_0 ER -
%0 Journal Article %A Alsedà, Lluis %A Llibre, J. %A Misiurewicz, M. %A Tresser, C. %T Periods and entropy for Lorenz-like maps %J Annales de l'Institut Fourier %D 1989 %P 929-952 %V 39 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1195/ %R 10.5802/aif.1195 %G en %F 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) no. 4, pp. 929-952. doi : 10.5802/aif.1195. https://aif.centre-mersenne.org/articles/10.5802/aif.1195/
[ALMM] Lower bounds for the topological entropy of continuous maps of the circle of degree one, Nonlinearity, 1 (1988), 463-479. | MR | Zbl
, , 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 | Zbl
, , and ,[ALM] Periodic orbits of maps of Y, Trans. Amer. Math. Soc., 313 (1989), 475-538. | MR | Zbl
, and ,[BGMY] Periodic points and topological entropy of one-dimensional maps, Springer, Lect. Notes in Math., 819 (1980), 18-39. | MR | Zbl
, , 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 | Zbl
, 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 | Zbl
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 | Zbl
,[H1] The maximal measure for linear mod. one transformations, J. London Math. Soc., 23 (1981), 92-112. | MR | Zbl
,[H2] Periodic points for piecewise monotonic transformation, Ergod. Th. and Dynam. Sys., 5 (1985), 237-256. | MR | Zbl
,[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 | Zbl
,[M2] Twist sets for maps of a circle, Ergod. Th. and Dynam. Sys., 4 (1984), 391-404. | MR | Zbl
,[M3] Rotation intervals for a class of maps of the real line into itself, Ergod. Th. and Dynam. Sys., 6 (1986), 117-132. | MR | Zbl
,[MS] Entropy of piecewise monotone mappings, Studia Math., 67 (1980), 45-63. | MR | Zbl
and ,[MT] On iterated maps of the interval, in Dynamical Systems, Ed. J. C. Alexander, Lecture Notes in Math., 1342 (1988), 465-563. | MR | Zbl
and ,[P] The Lorenz attractor and a related population model, Lect. Notes in Math., Springer, 729 (1979), 169-187. | MR | Zbl
,[R] Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar., 8 (1957), 477-493. | Zbl
,[RT] Rotation numbers for monotone functions on the circle, J. London Math. Soc., 34 (1986), 360-368. | MR | Zbl
and ,Cité par Sources :