Stable intersections of Cantor sets and homoclinic bifurcations

Carlos Gustavo T. de A. Moreira

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 6, page 741-781
  • ISSN: 0294-1449

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Moreira, Carlos Gustavo T. de A.. "Stable intersections of Cantor sets and homoclinic bifurcations." Annales de l'I.H.P. Analyse non linéaire 13.6 (1996): 741-781. <http://eudml.org/doc/78400>.

@article{Moreira1996,
author = {Moreira, Carlos Gustavo T. de A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Cantor sets; homoclinic bifurcation; stable intersection; hyperbolicity},
language = {eng},
number = {6},
pages = {741-781},
publisher = {Gauthier-Villars},
title = {Stable intersections of Cantor sets and homoclinic bifurcations},
url = {http://eudml.org/doc/78400},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Moreira, Carlos Gustavo T. de A.
TI - Stable intersections of Cantor sets and homoclinic bifurcations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 6
SP - 741
EP - 781
LA - eng
KW - Cantor sets; homoclinic bifurcation; stable intersection; hyperbolicity
UR - http://eudml.org/doc/78400
ER -

References

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  1. [BPV] R. Bamón, S. Plaza and J. Vera, On Central Cantor Sets with self-arithmetic difference of positive Lebesgue measure, to appear in J. London Math. Soc. Zbl0839.28002
  2. [H] M. Hall, On the sum and product of continued fractions, Annals of Math., Vol. 48, 1947, pp. 966-993. Zbl0030.02201MR22568
  3. [MO] P. Mendes and F. Oliveira, On the topological structure of the arithmetic sum of two Cantor sets, Nonlinearity, Vol. 7, 1994, pp. 329-343. Zbl0839.54027MR1267692
  4. [N1] S. Newhouse, Non density of Axiom A(a) on S2, Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 191-202. Zbl0206.25801MR277005
  5. [N2] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, Vol. 13, 1974, pp. 9-18. Zbl0275.58016MR339291
  6. [N3] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, Vol. 50, 1979, pp. 101-151. Zbl0445.58022MR556584
  7. [P] J. Palis, Homoclinic bifurcations, sensitive chaotic dynamics and strange attractors, Dynamical Syst. and Related Topics, World Scientific, 1991, pp. 466-473. MR1164908
  8. [PT] J. Palis and F. Takens, Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms, Invent. Math., Vol. 82, 1985, pp. 379-442. Zbl0579.58005MR811543
  9. [PT1] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math., Vol. 125, 1987, pp. 337-374. Zbl0641.58029MR881272
  10. [PT2] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: fractal dimensions and infinitely many attractors, Cambridge Univ. Press, 1992. Zbl0790.58014MR1237641
  11. [PY] J. Palis and J.C. Yoccoz, Homoclinic Tangencies for Hyperbolic sets of large Hausdorff Dimension Bifurcations, Acta Mathematica, Vol. 172, 1994, pp. 91-136. Zbl0801.58035MR1263999
  12. [S] A. Sannami, An example of a regular Cantor set whose difference set is a Cantor set with positive measure, Hokkaido Math. Journal, Vol. XXI (1), 1992, pp. 7-23. Zbl0787.58028MR1153749

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