A global view of dynamics and a conjecture on the denseness of finitude of attractors
Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995, Astérisque, no. 261 (2000), pp. 335-347.
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     author = {Palis, Jacob},
     title = {A global view of dynamics and a conjecture on the denseness of finitude of attractors},
     booktitle = {G\'eom\'etrie complexe et syst\`emes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995},
     editor = {Flexor Marguerite and Sentenac Pierrette and Yoccoz Jean-Christophe},
     series = {Ast\'erisque},
     pages = {335--347},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {261},
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Palis, Jacob. A global view of dynamics and a conjecture on the denseness of finitude of attractors, in Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995, Astérisque, no. 261 (2000), pp. 335-347. http://archive.numdam.org/item/AST_2000__261__335_0/

[ABV] J. F. Alves, C. Bonatti and M. Viana, SRB measures for partially hyperbolic systems: the expanding case, to appear in Invent. Math. | MR | Zbl

[A] J. F. Alves, SRB measures for nonhyperbolic systems with multidimensional expansion, thesis IMPA, 1997, to appear in Ann. Sci. ENS. | Numdam | Zbl

[Ar] V. I. Arnold, On the mapping of the circle into itself, Izvestia Akad. Nauk., USSR Math. Series bf 25 (1961), 21-86. | MR

[BC] M. Benedicks and L. Carleson, The dynamics of the Hénon maps, Ann. of Math. 133 (1991), 73-169. | DOI | MR | Zbl

[BV1] M. Benedicks and M. Viana, Solution of the basin problem for Hénon-like attractors, preprint 1999. | MR | Zbl

[BV2] M. Benedicks and M. Viana, Stochastic stability and other statistical properties for Hénon-like maps, in preparation.

[BY1] M. Benedicks and L.-S. Young, Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps, Ergod. Th. & Dynam. Sys. 12 (1992), 13-37. | DOI | MR | Zbl

[BY2] M. Benedicks and L.-S. Young, SBR-measures for certain Hénon maps, Invent. Math. 112 (1993), 541-576. | DOI | EuDML | MR | Zbl

[BD] C. Bonatti and L. J. Díaz, Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math. 143 (1996), 357-396. | DOI | MR | Zbl

[BPV] C. Bonatti, A. Pumariño, and M. Viana, Lorenz attractors with arbitrary expanding dimension, CR. Acad. Sci. Paris 325 (1997), 883-888. | MR | Zbl

[C] E. Colli, Infinitely many coexisting strange attractors, to appear, Annales de l'Inst. Henri Poincaré, 15 (1998), 539-579. | DOI | EuDML | Numdam | MR | Zbl

[C] E. Colli, Infinitely many coexisting strange attractors, to appear, Analyse Non linéaire 15 (1998), 539-579. | DOI | EuDML | Numdam | MR | Zbl

[CE1] E. Catsigeras and H. Enrich, Homoclinic tangencies near cascades of period doubling bifurcations, to appear, Ann. de l'Inst. Henri Poincaré Analyse Nonlinéaire. | EuDML | Numdam | MR | Zbl

[CE2] E. Catsigeras and H. Enrich, Persistence of the Feigenbaum attractor in oneparameter families, preprint 1997. | MR | Zbl

[CT] P. Coullet and C. Tresser, Iterations d'endomorphismes et groupe de renormalisation, CRAS Paris 287 (1978), 577-580. | MR | Zbl

[dMM] W. De Melo and M. Martens, Universal models for Lorenz maps, preprint 1997, to appear, Ergodic Th. and Dyn. Syst. | MR | Zbl

[dM] W. De Melo, Rigidity and renormalization in one-dimensional dynamics, Procs. International Congress of Mathematicians, ICM98-Berlin. | Zbl

[dMS] W. De Melo and S. Van Strien, One-dimensional dynamics, Springer-Verlag, 1993. | MR | Zbl

[DRV] L. J. Díaz, J. Rocha, and M. Viana, Strange attractors in saddle-node cycles: prevalence and globality, Invent. Math. 125 (1996), 37-74. | DOI | MR | Zbl

[DPU] L. J. Díaz, E. Pujals, and R. Ures, Normal hyperbolicity and robust transitivity, preprint 1997, to appear in Acta Math. | MR | Zbl

[F] M. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978), 25-52. | DOI | MR | Zbl

[GS] J. Graczyk and G. Swiatek, Generic hyperbolicity in the logistic family, Annals of Math. 146 (1997), 1-52. | DOI | MR | Zbl

[Ha] S. Hayashi, Connecting invariant manifolds and the solution of the C 1 stability and Ω-stability conjectures for flows, Annals of Math. 145 (1997), 81-137. | DOI | MR | Zbl

[He] M. Hénon, A two dimensional mapping with a strange attractor, Comm. Math. Phys. 50 (1976), 69-77. | DOI | MR | Zbl

[H] M. Herman. Sur la conjugaison différentiable des difféomorphims du cercle à des rotations, Publ. Math. 49 (1979), 5-233. | DOI | EuDML | Numdam | MR | Zbl

[J] M. Jacobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. | DOI | MR | Zbl

[K] Y. Kifer, Random perturbations of dynamical systems, Birkhäuser, 1988. | DOI | MR | Zbl

[Ko] O. Kozlovski, Structural stability in one-dimensional dynamics, PhD thesis, Univ. Amsterdam, 1997.

[L] E. N. Lorenz, Deterministic nonperiodic flow, J. Atmosph. Sci. 20 (1963), 130-141. | DOI | Zbl

[LP] R. Labarca and M. J. Pacifico, Stability of singular horseshoes, Topology 25 (1986), 337-352. | DOI | MR | Zbl

[LV1] S. Luzzatto and M. Viana, Positive Lyapunov exponents for Lorenz-like maps with criticalities, these proceedings. | Numdam | Zbl

[LV2] S. Luzzatto and M. Viana, Lorenz-like attractors without invariant foliations, in preparation.

[Ly1] M. Lyubich, Dynamics of quadratic polynomials I-II, Acta Math., 178 (1997), 185-297. | DOI | MR | Zbl

[Ly2] M. Lyubich, Almost every real quadratic map is either regular or stochastic, preprint 1997. | MR | Zbl

[M1] R. Mañe, Contribution to the stability conjecture, Topology 17 (1978), 383-396. | DOI | MR | Zbl

[M2] R. Mañe, A proof of the C 1 stability conjecture, Publ. Math. I.H.E.S. 66 (1987), 161-210. | DOI | EuDML | Numdam | MR | Zbl

[MN] M. Martens and T. Nowicki, Invariant measures for Lebesgue typical quadratic maps, these proceedings.

[Mor] C. Moreira, Stable intersections of Cantor sets and homoclinic bifurcations, Annales de l'Institut Henri Poincaré, Analyse Non Linéaire, vol. 13, n° 6, (1996), 741-781. | DOI | EuDML | Numdam | MR | Zbl

[MorY1] C. Moreira and J.-C. Yoccoz, Stable intersections of regular Cantor sets with large Hausdorff dimensions, preprint 1998. | MR | Zbl

[MorY2] C. Moreira and J.-C. Yoccoz, Stable homoclinic tangencies for hyperbolic sets of large Hausdorff dimension, in preparation.

[MV] L. Mora and M. Viana, Abundance of strange attractors, Acta Math. 171 (1993), 1-71. | DOI | MR | Zbl

[MPa] C. Morales and M. J. Pacifico, New singular strange attractors arising from hyperbolic systems, preprint 1997.

[MPu1] C. Morales and E. Pujals, Singular strange attractors on the boundary of Morse-Smale systems, Ann. Sci. E.N.S. 30 (1997), 693-718. | EuDML | Numdam | MR | Zbl

[MPu2] C. Morales and E. Pujals, Strange attractors containing a singularity with two positive multipliers, Comm. Math. Phys. 196 (1998), 671-679. | DOI | MR | Zbl

[MPP1] C. Morales, M. J. Pacifico, and E. Pujals, New strange attractors on the boundary of hyperbolic systems, preprint 1997. | Zbl

[MPP2] C. Morales, M. J. Pacifico, and E. Pujals, Global attractors from the explosion of singular cycles, CR. Acad. Sci. Paris 325 (1997), 1317-1322. | MR | Zbl

[MPP3] C. Morales, M. J. Pacifico, and E. Pujals, Singular hyperbolic sets, Proc. Amer. Math. Soc. 127 (1999), 3343-3400. | MR | Zbl

[MPP4] C. Morales, M. J. Pacifico, and E. Pujals, On C 1 robust singular transitive sets for three-dimensional flows, CR. Acad. Sci. Paris 326 (1998), 81-86. | MR | Zbl

[N] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. I.H.E.S. 50 (1979), 101-151. | DOI | EuDML | Numdam | MR | Zbl

[PRV1] M. J. Pacifico, A. Rovella, and M. Viana, Infinite-modal maps with global chaotic behavior, Annals of Math. 148 (1998), 441-484. | DOI | MR | Zbl

[PRV2] M. J. Pacifico, A. Rovella, and M. Viana, Persistence of global spiraling attractors, in preparation.

[PS] E. Pujals and M. Sambarino, Homoclinic tangencies and hyperbolicity for surface diffeomorphisms: A conjecture of Palis, preprint 1998, to appear in Annals of Math. | EuDML | Zbl

[PSh] C. Pugh and M. Shub, Stable ergodicity and julienne quasi-conformality, preprint 1997. | MR | Zbl

[PT] J. Palis and F. Takens, Hyperbolicity and sensitive-chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. | MR | Zbl

[PT1] J. Palis and F. Takens, Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms, Inventiones Math. 82 (1985), 397-422. | DOI | EuDML | MR | Zbl

[PT2] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math. 125 (1987), 337-374. | DOI | MR | Zbl

[PV] J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many periodic attractors, Annals of Math. 140 (1994), 207-250. | DOI | MR | Zbl

[PY1] J. Palis and J.-C. Yoccoz, Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension, Acta Mathematica, vol. 172 (1994), 91-136. | DOI | MR | Zbl

[PY2] J. Palis and J.-C. Yoccoz, Non-uniform hyperbolic horseshoes arising from homoclinic bifurcations, to appear in CR. Acad. Sci. Paris.

[R] A. Rovella, The dynamics of perturbations of the contracting Lorenz attractor, Bull. Braz. Math. Soc. vol. 24, n° 2 (1993), 233-259. | DOI | MR | Zbl

[S] M. Shub, Topological transitive diffeomorphisms on ^T 4 , Lecture Notes in Math. 206 (1971), 39, Springer-Verlag.

[TY] L. Tedeschini-Lalli and J. A. Yorke, How often do simple dynamical processes have infinitely many coexisting sinks? Comm. Math. Phys. 106 (1986), 635-657. | DOI | MR | Zbl

[U] R. Ures, On the approximation of Hénon-like attractors by homoclinic tangencies, Ergodic Theory and Dynamical Systems, vol. 15 (1995), 1223-1230. | DOI | MR | Zbl

[V1] M. Viana, Multidimensional nonhyperbolic attractors, Publ. Math. IHES (1997). | EuDML | MR | Zbl

[V2] M. Viana, Dynamics: a probabilistic and geometric perspective, Procs. International Congress of Mathematicians, ICM98-Berlin. | Zbl