Saddle-focus singular cycles and prevalence of hyperbolicity

Bernardo San Martín

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 5, page 623-649
  • ISSN: 0294-1449

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San Martín, Bernardo. "Saddle-focus singular cycles and prevalence of hyperbolicity." Annales de l'I.H.P. Analyse non linéaire 15.5 (1998): 623-649. <http://eudml.org/doc/78450>.

@article{SanMartín1998,
author = {San Martín, Bernardo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {unfolding; vector field; saddle-focus singular cycle; hyperbolicity},
language = {eng},
number = {5},
pages = {623-649},
publisher = {Gauthier-Villars},
title = {Saddle-focus singular cycles and prevalence of hyperbolicity},
url = {http://eudml.org/doc/78450},
volume = {15},
year = {1998},
}

TY - JOUR
AU - San Martín, Bernardo
TI - Saddle-focus singular cycles and prevalence of hyperbolicity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 5
SP - 623
EP - 649
LA - eng
KW - unfolding; vector field; saddle-focus singular cycle; hyperbolicity
UR - http://eudml.org/doc/78450
ER -

References

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  2. [2] L. Mora and M. Viana, Abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-71. Zbl0815.58016MR1237897
  3. [3] S. Newhouse and J. Palis ;Cycles and bifurcation theory, Ast'erisque, Vol. 31, 1976, pp. 293-301. Zbl0322.58009MR516408
  4. [4] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable set for diffeomorphisms, Publ. Math. I.H.E.S, Vol. 50, 1979, pp. 101-151. Zbl0445.58022MR556584
  5. [5] S. Newhouse, J. Palis and F. Takens, Bifurcations and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., Vol. 57, 1983, pp. 5-71. Zbl0518.58031MR699057
  6. [6] M.J. Pacifico and A. Rovella, Unfolding contracting cycles, Ann. Scient. Ec. Norm. Sup., 4e serie t. 26, 1993, pp. 691-700. Zbl0802.58036MR1251149
  7. [7] J. Palis and F. Takens, Cycles and measure of bifurcation sets for two-dimensional diffeomorphims, Inventiones Math., Vol. 82, 1985, pp. 397-422. Zbl0579.58005MR811543
  8. [8] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math., Vol. 125, 1987, pp. 337-374. Zbl0641.58029MR881272
  9. [9] J. Palis and F. Takens, Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations, Cambridge studies in advanced mathematics, Vol. 35. Zbl0790.58014
  10. [10] A. Rovella, The Dynamics of Perturbations of the contracting Lorenz attractor, Bol. Soc. Bras. Math., Vol. 24, No. 2, 1993, pp. 233-259. Zbl0797.58051MR1254985
  11. [11] B. San Martin, Contracting singular cycles. To appears. Zbl0942.37039
  12. [12] C. Tresser, About some theorems by L. P. Sil'nikov, Annals Inst. Henri Poincare., Vol. 40 No. 4, 1984, pp. 441-461. Zbl0556.58025MR757766
  13. [13] E. Wiggins, Global bifurcations and chaos, Applied. Mathematical Sciences, Vol. 73, Springer Verlag, pp. 301-306. Zbl0661.58001

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