Abstract
Roughly speaking, Peixoto’s foundationalworks in the global theory of ordinary dif- ferential equations corresponds to the papers [17–19] which are nowadays referred to as Peixoto’s Theorem.
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References
Avila A., de Melo, W., Lyubich, M.: Regular or stochastic dynamics in real analytic families of unimodal maps. Invent. Math. 154, 451–550 (2003)
Avila, A., Moreira, C.: Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Contemp. Math. 389, 1–42
Avila, A., Moreira, C.: Statistical properties of unimodal maps: the quadratic family. Ann. Math. 161, 831–881
Anosov, D.V.: Geodesic flows on closed riemannian manifolds with negative curvature. Proc. Steklov Inst. of Math. (translated by the AMS) 90 (1967)
Benedicks, M., Carleson, L.: The dynamics of the Hénon map. Ann. Math. 133, 73–169 (1991)
Bonatti, C., Diaz, L.J.: Persistence of transitive diffeomorphisms. Ann. Math. 143, 367–396 (1995)
Colli, E.: Infinitely many coexisting strange attractors. Annales de l’Inst. Henri Poincaré, Analyse Nonlinéaire (in press)
Crovisier, S., Pujals, E.R.: Homoclinic bifurcations and essentially hyperbolicity. preprint
Diaz, L.J.: Robust nonhyperbolic dynamics at heterodimensional cycles. Ergod.Theory Dyn. Syst. 15, 291–315 (1995)
Diaz, L.J.: Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations. Nonlinearity 8, 693–715 (1995)
Kozlovski, O., Shen, W., van Strien, S.: Density of hyperbolicity in dimension one. Ann. Math. 166, 145–182 (2007)
Lyubich, M.: Almost every real quadratic map is either regular or stochastic. Ann. Math. 156, 1–78
Mora, L., Viana, M.: Abundance of strange attractors. Acta Math. 171, 1–71 (1993)
Newhouse, S.: Non-density of Axiom A(a) on S 2.Proc. A.M.S. Symp. Pure Math. 14, 191–202 (1970)
Newhouse, S.: Diffeomorphism with infinitely many sinks. Topology 13, 9–18 (1974)
Newhouse, S.: The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms. Publ. Math. I.H.E.S. 50, 101–151 (1979)
Peixoto, M.: On structural stability. Ann. Math. 69, 199–222 (1959)
Peixoto, M.: Structural stability in the plane with enlarged boundary conditions. Anais da Academia Brasileira de Ciencias 31, 135–160 (1959). (in collaboration with M.C. Peixoto)
Peixoto, M.: Structural stability on two-dimensional manifolds. Topology 1(1962) pp. 101–120.
Palis, J.: Homoclinic orbits, hyperbolic dynamics and dimension of Cantor sets. The Lefschetz centennial conference. Contemp. Math., 58, III, (1984) 203–216
Palis, J.: A global view of dynamics and a conjecture on the denseness of finitude of attractors. Gemetrie complexe et systemes dynamiques (Orsay, 1995). Asterisque 261, 335–347 (2000)
Pujals, E.R., Sambarino, M.: Homoclinic tangencies and hyperbolicity for surface diffeomorphisms. Ann. Math. 151, 961–1023 (2000)
Pujals, E.R., Sambarino, M.: On the dynamic of dominated splitting. Ann. Math. 169, 675–740 (2009)
J.Palis and F.Takens Hyperbolicity and sensitive-chaotic dynamics at homoclinic bifurcationsCambridge University Press, 1993.
Shub, M.: Topologically transitive diffeomorphism of T 4. In: Symposium on Differential Equations and Dynamical Systems (University of Warwick, 1968/69), pp. 39–40. Lecture Notes in Math., vol. 206. Springer, Berlin (1971)
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Pujals, E.R. (2011). From Peixoto’s Theorem to Palis’s Conjecture. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science I. Springer Proceedings in Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11456-4_47
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