Persistent homoclinic tangencies and the unfolding of cycles

Lorenzo J. Díaz; Raúl Ures

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 6, page 643-659
  • ISSN: 0294-1449

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Díaz, Lorenzo J., and Ures, Raúl. "Persistent homoclinic tangencies and the unfolding of cycles." Annales de l'I.H.P. Analyse non linéaire 11.6 (1994): 643-659. <http://eudml.org/doc/78347>.

@article{Díaz1994,
author = {Díaz, Lorenzo J., Ures, Raúl},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {bifurcation; cycle; heteroclinic point; homoclinic tangency; hyperbolic},
language = {eng},
number = {6},
pages = {643-659},
publisher = {Gauthier-Villars},
title = {Persistent homoclinic tangencies and the unfolding of cycles},
url = {http://eudml.org/doc/78347},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Díaz, Lorenzo J.
AU - Ures, Raúl
TI - Persistent homoclinic tangencies and the unfolding of cycles
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 6
SP - 643
EP - 659
LA - eng
KW - bifurcation; cycle; heteroclinic point; homoclinic tangency; hyperbolic
UR - http://eudml.org/doc/78347
ER -

References

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  2. [2] L.J. Diaz, Robust nonhyperbolic dynamics and the creation of heterodimensional cycles, Erg. Th. and Dyn. Sys. (to appear). Zbl0831.58035
  3. [3] L.J. Diaz, Persistence of heteroclinic cycles and nonhyperbolic dynamics at the unfolding of heteroclinic bifurcations, preprint. Zbl0836.58031
  4. [4] L.J. Diaz, and J. Rocha, Non-connected heterodimensional cycles: bifurcation and stability, Nonlinearity, Vol. 5, 1992, pp. 1315-1341. Zbl0780.58033MR1192520
  5. [5] L.J. Diaz, Hyperbolicity and the creation of heterodimensional cycles, in preparation. 
  6. [6] L.J. Diaz, J. Rocha and M. Viana, Prevalence of strange attractors and critical saddle-node cycles, preprint. Zbl0865.58034
  7. [7] L. Mora and M. Viana, The abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-72. Zbl0815.58016MR1237897
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  9. [9] S. Newhouse, The abundance of wild hyperbolic sets and non smooth stable sets for diffeomorphisms, Publ. I.H.E.S., Vol. 50, 1979, pp. 101-151. Zbl0445.58022MR556584
  10. [10] S. Newhouse and J. Palis , Cycles and bifurcation theory, Publ. Asterisque, Vol. 31, 1976 pp. 44-140. Zbl0322.58009MR516408
  11. [11] S. Newhouse, J. Palis and F. Takens , Bifurcations and stability of families of diffeomorphisms, Publ. I.H.E.S. , Vol. 57, 1983, pp. 5-71. Zbl0518.58031MR699057
  12. [12] J. Palis and F. Takens , Hyperbolicity and the creation of homoclinic orbits, Ann. of Math., Vol. 125, 1987, pp. 337-374. Zbl0641.58029MR881272
  13. [13] J. Palis and F. Takens , Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations, Fractal Dimensions and Infinitely Many Attractors, Cambridge University Press, 1993. Zbl0790.58014MR1237641
  14. [14] J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many sinks, Ann. of Math. (to appear). Zbl0817.58004
  15. [15] J. Palis and J.C. Yoccoz, Homoclinic bifurcations: Large Haussdorf dimension and non-hyperbolic behaviour, Acta Math., Vol. 172, 1994, pp. 91-136. Zbl0801.58035MR1263999
  16. [16] N. Romero, Persistence of homoclinic tangencies in higher dimension, Erg. Th. and Dyr. Sys. (to appear). Zbl0833.58020MR1346398
  17. [17] F. Takens, Partially hyperbolic fixed points, Topology, Vol. 8, 1971, pp. 133-147. Zbl0214.22901MR307279
  18. [18] M. Viana, Strange attractors in higher dimensions, Bol. Soc. Bras. Mat., Vol. 24, 1993, pp. 13-62. Zbl0784.58044MR1224299

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