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 inIsrael J. Math.
Carvalho, M., Sinai-Ruelle-Bowen measures forN-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, inDynamical 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 theC 1-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 theC 1 stability conjecture.Inst. Hautes Études Sci. Publ. Math., 66 (1988), 161–210.
Morales, C., Pacífico, M. J. &Pujals, E. R., OnC 1 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 ofT 4, inSymposium 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, inGlobal Analysis (Berkeley, CA, 1968), pp. 329–334. Proc. Sympos. Pure Math., 14. Amer. Math. Soc., Providence, RI, 1970.
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This work is partially supported by CNPq, PRONEX-Dynamical Systems and FAPERJ (Brazil), and CSIC and CONICYT (Uruguay).
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Díaz, L.J., Pujals, E.R. & Ures, R. Partial hyperbolicity and robust transitivity. Acta Math 183, 1–43 (1999). https://doi.org/10.1007/BF02392945
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DOI: https://doi.org/10.1007/BF02392945