Nonhyperbolic persistent attractors near the Morse-Smale boundary
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 5, pp. 867-888.
@article{AIHPC_2003__20_5_867_0,
     author = {Mu\~noz Morales, Eduardo M and San Mart{\'\i}n Rebolledo, Bernardo and Vera Valenzuela, Jaime A},
     title = {Nonhyperbolic persistent attractors near the {Morse-Smale} boundary},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {867--888},
     publisher = {Elsevier},
     volume = {20},
     number = {5},
     year = {2003},
     doi = {10.1016/S0294-1449(03)00015-5},
     zbl = {01975937},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0294-1449(03)00015-5/}
}
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Muñoz Morales, Eduardo M; San Martín Rebolledo, Bernardo; Vera Valenzuela, Jaime A. Nonhyperbolic persistent attractors near the Morse-Smale boundary. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 5, pp. 867-888. doi : 10.1016/S0294-1449(03)00015-5. http://www.numdam.org/articles/10.1016/S0294-1449(03)00015-5/

[1] Benedicks M., Carleson L., On iterations of 1−ax2 on (−1,1), Ann. Math. 122 (1985) 1-24. | Zbl

[2] Benedicks M., Carleson L., The dynamics of the Hénon map, Ann. Math. 133 (1991) 73-169. | MR | Zbl

[3] Bamón R., Labarca R., Mañé R., Pacífico M.J., The explosion of singular cycles, Publ. Math. IHES 78 (1993) 207-232. | EuDML | Numdam | MR | Zbl

[4] Collet P., Eckmann J.P., On the abundance of aperiodic behaviour for maps on the interval, Comm. Phys. 73 (1980) 115-160. | MR | Zbl

[5] Guckenheimer J., Sensitive dependence to initial conditions for one dynamical maps, Comm. Math. Phys. 70 (1979) 133-160. | MR | Zbl

[6] Labarca R., Bifurcation of contracting singular cycles, Ann. Scient. Ec. Norm. Sup. 4e Série 28 (1995) 705-745. | EuDML | Numdam | MR | Zbl

[7] Labarca R., Pacífico M.J., Stability of singular horseshoe, Topology 25 (1986) 337-352. | MR | Zbl

[8] De Mello W., Van Strien S., One-Dimensional Dynamics, Modern Surveys in Mathematics, 25, Springer-Verlag, Berlin, 1991. | Zbl

[9] C. Morales, M.J. Pacifico, B. San Martín, Lorenz atractor from double homoclinic resonant cycles, Preprint.

[10] Mora L., Viana M., Abundance of strange attractors, Acta Math. 171 (1993) 1-71. | MR | Zbl

[11] Pacífico M.J., Rovella A., Unfolding contracting singular cycles, Ann. Scient. Éc. Norm. Sup. 4e Série 26 (1993) 691-700. | EuDML | Numdam | MR | Zbl

[12] Palis J., On Morse-Smale dynamical systems, Topology 8 (1969). | MR | Zbl

[13] Palis J., Smale S., Structural Stability Theorems, Global Analysis, Proc. Symp. in Pure Math., XIV, American Mathematical Society, Providence, RI, 1970. | MR | Zbl

[14] Palis J., Takens F., Hyperbolicity & Sensitive Chaotic Dynamics at Homoclinic Bifurcations, Cambridge Studies in Advanced Mathematics, 35, Cambridge University Press, Cambridge, 1993. | MR | Zbl

[15] A. Rovella, The dynamics of perturbations of the contracting Lorenz attractor, Bol. Soc. Bras. Mat. 24 (2) 233-259. | MR | Zbl

[16] San Martín B., Contracting singular cycles, Ann. Inst. Henri Poincaré 15 (5) (1998) 651-659. | EuDML | Numdam | MR | Zbl

[17] B. San Martín, J. Vera, Nonhyperbolic persistent attractors near the Morse-Smale boundary II, Informe de matemáticas UCN.

[18] Shub M., Global Stability of Dynamical Systems, Springer-Verlag, Berlin, 1987. | MR | Zbl

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