Abundance of hyperbolicity in the C 1 topology

Raúl Ures

Annales scientifiques de l'École Normale Supérieure (1995)

  • Volume: 28, Issue: 6, page 747-760
  • ISSN: 0012-9593

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Ures, Raúl. "Abundance of hyperbolicity in the $C^1$ topology." Annales scientifiques de l'École Normale Supérieure 28.6 (1995): 747-760. <http://eudml.org/doc/82401>.

@article{Ures1995,
author = {Ures, Raúl},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {6},
pages = {747-760},
publisher = {Elsevier},
title = {Abundance of hyperbolicity in the $C^1$ topology},
url = {http://eudml.org/doc/82401},
volume = {28},
year = {1995},
}

TY - JOUR
AU - Ures, Raúl
TI - Abundance of hyperbolicity in the $C^1$ topology
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1995
PB - Elsevier
VL - 28
IS - 6
SP - 747
EP - 760
LA - eng
UR - http://eudml.org/doc/82401
ER -

References

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  1. [AS] R. ABRAHAM and S. SMALE, Non-genericity of Ω-stability (Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970). Zbl0215.25102MR42 #6867
  2. [AM] A. ARAÚJO and R. MAÑ;É, On the existence of hyperbolic attractors and homoclinic tangencies for surfaces diffeomorphisms (to appear). 
  3. [M1] R. MAÑ;É, Contribution to the stability conjecture (Topology, Vol. 17, 1978, pp. 383-396). Zbl0405.58035MR84b:58061
  4. [M2] R. MAÑ;É, A proof of the C1 stability conjecture (Publ. I.H.E.S., Vol. 66, 1988, pp. 161-210). Zbl0678.58022
  5. [MM] A. MANNING and H. MCCLUSKEY, Hausdorff dimension for horseshoes (Erg. Th. and Dyn. Syst., Vol. 3, 1983, pp. 251-261). Zbl0529.58022MR85j:58127
  6. [N1] S. NEWHOUSE, Nondensity of Axiom A (a) on S2 (Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 191-202). Zbl0206.25801MR43 #2742
  7. [N2] S. NEWHOUSE, Diffeomorphisms with infinitely many sinks (Topology, Vol. 13, 1974, pp. 9-18). Zbl0275.58016MR49 #4051
  8. [N3] 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). Zbl0445.58022MR82e:58067
  9. [P] J. PALIS, On the C1 Ω-stability conjecture (Publ. I.H.E.S., Vol. 66, 1988, pp. 211-215). Zbl0648.58019MR89e:58091
  10. [PT1] J. PALIS and F. TAKENS, Hyperbolicity and sensitive-chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. Zbl0790.58014MR94h:58129
  11. [PT2] J. PALIS and F. TAKENS, Hyperbolicity and the creation of homoclinic orbits (Ann. of Math., Vol. 125, 1987, pp. 337-374). Zbl0641.58029MR89b:58118
  12. [PV] J. PALIS and M. VIANA, Continuity of Hausdorff dimension and limit capacity for horseshoes, Dynamical Systems (Lecture Notes in Math., Vol. 1331, 1988, pp. 150-160). Zbl0661.58023MR89k:58231
  13. [PY] J. PALIS and J. C. YOCCOZ, Homoclinic bifurcations : Large Hausdorff dimension and non-hyperbolic behaviour (Acta Math., to appear). 
  14. [S] C. SIMON, Instability in Diff1 (T3) (Lecture Notes in Math., Vol. 206, 1971, pp. 94-97). 
  15. [W] R. WILLIAMS, The "DA" maps of Smale and structural stability (Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 329-334). Zbl0213.50303MR41 #9296

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