Acta Mathematica

Partial hyperbolicity and robust transitivity

Lorenzo J. Díaz, Enrique R. Pujals, and Raúl Ures

Full-text: Open access

Note

This work is partially supported by CNPq, PRONEX-Dynamical Systems and FAPERJ (Brazil), and CSIC and CONICYT (Uruguay).

Article information

Source
Acta Math. Volume 183, Number 1 (1999), 1-43.

Dates
Received: 20 April 1998
Revised: 8 April 1999
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891247

Digital Object Identifier
doi:10.1007/BF02392945

Zentralblatt MATH identifier
0987.37020

Rights
1999 © Institut Mittag-Leffler

Citation

Díaz, Lorenzo J.; Pujals, Enrique R.; Ures, Raúl. Partial hyperbolicity and robust transitivity. Acta Math. 183 (1999), no. 1, 1--43. doi:10.1007/BF02392945. https://projecteuclid.org/euclid.acta/1485891247.


Export citation

References

  • Bonatti, Ch., Seminar, IMPA, 1996.
  • Bonatti, Ch. & Díaz, L. J., Persistence of transitive diffeomorphisms. Ann. of Math., 143 (1995), 367–396.
  • —, Connexions hétérocliniques et généricité d’une infinité de puits ou de sources. Ann. Sci. École Norm. Sup., 32 (1999), 135–150.
  • Bonatti, Ch. & Viana, M., SRB measures for partially hyperbolic atractors: the contracting case. To appear in Israel J. Math.
  • Carvalho, M., Sinai-Ruelle-Bowen measures for N-dimensional derived from Anosov diffeomorphisms. Ergodic Theory Dynamical Systems, 13 (1993), 21–44.
  • Camacho, C. & Lins Neto, A., Geometric Theory of Foliations, Birkhäuser Boston, Boston, MA, 1985.
  • Díaz, L. J., Robust nonhyperbolic dynamics at heterodimensional cycles. Ergodic Theory Dynamical Systems, 15 (1995), 291–315.
  • —, Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations. Nonlinearity, 8 (1995), 693–715.
  • Doering, C. I., Persistently transitive vector fields on three-dimensional manifolds, in Dynamical Systems and Bifurcation Theory (Rio de Janeiro, 1985), pp. 59–89. Pitman Res. Notes Math. Ser., 160, Longman Sci. Tech., Harlow, 1987.
  • Díaz, L. J. & Rocha, J., Noncritical saddle-node cycles and robust nonhyperbolic dynamics. Dynamics Stability Systems, 12 (1997), 109–135.
  • Díaz, L. J. & Ures, R., Persistent homoclinic tangencies and the unfolding of cycles. Ann. Inst. H. Poincaré Anal. Non Linéaire, 11 (1994), 643–659.
  • Franks, J., Necessary conditions for the stability of diffeomorphisms. Trans. Amer. Math. Soc., 158 (1971), 301–308.
  • Grayson, M., Pugh, C. & Shub, M., Stably ergodic diffeomorphisms. Ann. of Math., 140 (1994), 295–329.
  • Hayashi, S., Connecting invariant manifolds and the solution of the C1-stability and Ω-stability conjectures for flows. Ann. of Math., 145 (1997), 81–137.
  • Hirsch, M., Pugh, C. & Shub, M., Invariant Manifolds, Lecture Notes in Math., 583. Springer-Verlag, Berlin-New York, 1977.
  • Mañé, R., Contributions to the stability conjecture. Topology, 17 (1978), 386–396.
  • —, Persistent manifolds are normally hyperbolic. Trans. Amer. Math. Soc., 246 (1978). 261–283.
  • —, An ergodic closing lemma. Ann. of Math., 116 (1982), 541–558.
  • —, A proof of the C1 stability conjecture. Inst. Hautes Études Sci. Publ. Math., 66 (1988), 161–210.
  • Morales, C., Pacífico, M. J. & Pujals, E. R., On C1 robust singular transitive sets for three-dimensional flows. C. R. Acad. Sci. Paris Sér. I Math., 326 (1998), 81–86.
  • Newhouse, S., Codimension one Anosov diffeomorphisms. Amer. J. Math., 92 (1970), 761–770.
  • Pugh, C., The closing lemma. Amer. J. Math., 89 (1967), 956–1009.
  • Palis, J. & Viana, M., High-dimensional diffeomorphisms displaying infinitely many sinks. Ann. of Math., 140 (1994), 207–250.
  • Romero, N., Persistence of homoclinic tangencies in higher dimension. Ergodic Theory Dynamical Systems, 15 (1995), 735–759.
  • Shub, M., Topologically transitive diffeomorphism of T4, in Symposium on Differential Equations and Dynamical Systems (University of Warwick, 1968/69), pp. 39–40. Lecture Notes in Math., 206. Springer-Verlag, Berlin-New York, 1971.
  • Smale, S., Differentiable dynamical systems. Bull. Amer. Math. Soc., 73 (1967), 147–817.
  • Williams, R. F., The “DA” maps of Smale and structural stability, in Global Analysis (Berkeley, CA, 1968), pp. 329–334. Proc. Sympos. Pure Math., 14. Amer. Math. Soc., Providence, RI, 1970.