We study the non-wandering set of contracting Lorenz maps. We show that if such a map f doesn't have any attracting periodic orbit, then there is a unique topological attractor. Furthermore, we classify the possible kinds of attractors that may occur.
@article{AIHPC_2018__35_5_1409_0, author = {Brand\~ao, Paulo}, title = {Topological attractors of contracting {Lorenz} maps}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1409--1433}, publisher = {Elsevier}, volume = {35}, number = {5}, year = {2018}, doi = {10.1016/j.anihpc.2017.12.001}, mrnumber = {3813969}, zbl = {1393.37014}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2017.12.001/} }
TY - JOUR AU - Brandão, Paulo TI - Topological attractors of contracting Lorenz maps JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 1409 EP - 1433 VL - 35 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2017.12.001/ DO - 10.1016/j.anihpc.2017.12.001 LA - en ID - AIHPC_2018__35_5_1409_0 ER -
%0 Journal Article %A Brandão, Paulo %T Topological attractors of contracting Lorenz maps %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 1409-1433 %V 35 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2017.12.001/ %R 10.1016/j.anihpc.2017.12.001 %G en %F AIHPC_2018__35_5_1409_0
Brandão, Paulo. Topological attractors of contracting Lorenz maps. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1409-1433. doi : 10.1016/j.anihpc.2017.12.001. http://www.numdam.org/articles/10.1016/j.anihpc.2017.12.001/
[1] A possible new mechanism for the onset of turbulence, Phys. Lett. A, Volume 81A (1981) no. 4, pp. 197–201 | DOI | MR
[2] On the appearance and structure of the Lorenz attractor, Dokl. Acad. Sci. USSR (1977) no. 234, pp. 336–339 | MR | Zbl
[3] Wandering intervals for Lorenz maps with bounded nonlinearity, Bull. Lond. Math. Soc. (1991) no. 23, pp. 183–189 | MR | Zbl
[4] Une remarque sur la structure des endormorphismes de degré 1 du cercle, C. R. Acad. Sci. Paris, Ser. I, Volume 299 (1984) no. 5 | MR | Zbl
[5] New universal scenarios for the onset of chaos in Lorenz-type flows, Phys. Rev. Lett., Volume 57 (1986), pp. 925–928 | DOI | MR
[6] Dynamique régulière ou chaotique. Applications du cercle ou de l'intervalle ayant une discontinuité, C. R. Acad. Sci. Paris, Ser. I, Volume 300 (1985) no. 10, pp. 311–313 | MR | Zbl
[7] Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. (1979) no. 50, pp. 59–72 | Numdam | MR | Zbl
[8] Topological and measurable dynamics of Lorenz maps, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer Berlin Heidelberg, Berlin, Heidelberg, 2001, pp. 333–361 | DOI | MR | Zbl
[9] Essential dynamics for Lorenz maps on the real line and the lexicographical world, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 23 (2006), pp. 683–694 | Numdam | MR | Zbl
[10] Deterministic nonperiodic flow, J. Atmos. Sci., Volume 20 (1963) no. 2, pp. 130–141 | DOI | MR | Zbl
[11] Universal models for Lorenz maps, Ergod. Theory Dyn. Syst., Volume 21 (2001) no. 3, pp. 833–860 | DOI | MR | Zbl
[12] Hyperbolicity, sinks and measure in one dimensional dynamics, Commun. Math. Phys., Volume 100 (1985) no. 4, pp. 495–524 (Erratum) | DOI | Zbl
[13] One Dimensional Dynamics, Springer-Verlag, 1993 | MR | Zbl
[14] On the concept of attractor, Commun. Math. Phys., Volume 99 (1985), pp. 177–195 | DOI | MR | Zbl
[15] The dynamics of perturbations of the contracting Lorenz attractor, Bull. Braz. Math. Soc., Volume 24 (1993) no. 2, pp. 233–259 | DOI | MR | Zbl
[16] Topological and measurable dynamics of Lorenz maps, Diss. Math., Volume 382 (1999), pp. 1–134 | MR | Zbl
[17] Splitting words and Lorenz braids, Physica D, Volume 62 (1993), pp. 15–21 | DOI | MR | Zbl
Cité par Sources :