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), 13 p.
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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},
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year = {2000},
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Palis, Jacob. A global view of dynamics and a conjecture on the denseness of finitude of attractors, dans Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995, Astérisque, no. 261 (2000), 13 p. http://www.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 1757000 | Zbl 0962.37012

[A] J. F. Alves, SRB measures for nonhyperbolic systems with multidimensional expansion, thesis IMPA, 1997, to appear in Ann. Sci. ENS. | Numdam | Zbl 0955.37012

[Ar] V. I. Arnold, On the mapping of the circle into itself, Izvestia Akad. Nauk., USSR Math. Series bf 25 (1961), 21-86. | MR 140699

[BC] M. Benedicks and L. Carleson, The dynamics of the Hénon maps, Ann. of Math. 133 (1991), 73-169. | Article | MR 1087346 | Zbl 0724.58042

[BV1] M. Benedicks and M. Viana, Solution of the basin problem for Hénon-like attractors, preprint 1999. | MR 1835392 | Zbl 0967.37023

[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. | Article | MR 1162396 | Zbl 0769.58051

[BY2] M. Benedicks and L.-S. Young, $SBR$-measures for certain Hénon maps, Invent. Math. 112 (1993), 541-576. | Article | EuDML 144113 | MR 1218323 | Zbl 0796.58025

[BD] C. Bonatti and L. J. Díaz, Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math. 143 (1996), 357-396. | Article | MR 1381990 | Zbl 0852.58066

[BPV] C. Bonatti, A. Pumariño, and M. Viana, Lorenz attractors with arbitrary expanding dimension, CR. Acad. Sci. Paris 325 (1997), 883-888. | MR 1485910 | Zbl 0896.58043

[C] E. Colli, Infinitely many coexisting strange attractors, to appear, Annales de l'Inst. Henri Poincaré, 15 (1998), 539-579. | Article | EuDML 78448 | Numdam | MR 1643393 | Zbl 0932.37015

[C] E. Colli, Infinitely many coexisting strange attractors, to appear, Analyse Non linéaire 15 (1998), 539-579. | Article | EuDML 78448 | Numdam | MR 1643393 | Zbl 0932.37015

[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 78438 | Numdam | MR 1629345 | Zbl 0912.58025

[CE2] E. Catsigeras and H. Enrich, Persistence of the Feigenbaum attractor in oneparameter families, preprint 1997. | MR 1727238 | Zbl 0983.37046

[CT] P. Coullet and C. Tresser, Iterations d'endomorphismes et groupe de renormalisation, CRAS Paris 287 (1978), 577-580. | MR 512110 | Zbl 0402.54046

[dMM] W. De Melo and M. Martens, Universal models for Lorenz maps, preprint 1997, to appear, Ergodic Th. and Dyn. Syst. | MR 1836435 | Zbl 1108.37300

[dM] W. De Melo, Rigidity and renormalization in one-dimensional dynamics, Procs. International Congress of Mathematicians, ICM98-Berlin. | Zbl 0914.58016

[dMS] W. De Melo and S. Van Strien, One-dimensional dynamics, Springer-Verlag, 1993. | MR 1239171 | Zbl 0791.58003

[DRV] L. J. Díaz, J. Rocha, and M. Viana, Strange attractors in saddle-node cycles: prevalence and globality, Invent. Math. 125 (1996), 37-74. | Article | MR 1389960 | Zbl 0865.58034

[DPU] L. J. Díaz, E. Pujals, and R. Ures, Normal hyperbolicity and robust transitivity, preprint 1997, to appear in Acta Math. | MR 1719547 | Zbl 0987.37020

[F] M. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978), 25-52. | Article | MR 501179 | Zbl 0509.58037

[GS] J. Graczyk and G. Swiatek, Generic hyperbolicity in the logistic family, Annals of Math. 146 (1997), 1-52. | Article | MR 1469316 | Zbl 0936.37015

[Ha] S. Hayashi, Connecting invariant manifolds and the solution of the ${C}^{1}$ stability and $\Omega$-stability conjectures for flows, Annals of Math. 145 (1997), 81-137. | Article | MR 1432037 | Zbl 0871.58067

[He] M. Hénon, A two dimensional mapping with a strange attractor, Comm. Math. Phys. 50 (1976), 69-77. | Article | MR 422932 | Zbl 0576.58018

[H] M. Herman. Sur la conjugaison différentiable des difféomorphims du cercle à des rotations, Publ. Math. 49 (1979), 5-233. | Article | EuDML 103958 | Numdam | MR 538680 | Zbl 0448.58019

[J] M. Jacobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. | Article | MR 630331 | Zbl 0497.58017

[K] Y. Kifer, Random perturbations of dynamical systems, Birkhäuser, 1988. | Article | MR 1015933 | Zbl 0659.58003

[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. | Article | Zbl 06851676

[LP] R. Labarca and M. J. Pacifico, Stability of singular horseshoes, Topology 25 (1986), 337-352. | Article | MR 842429 | Zbl 0611.58033

[LV1] S. Luzzatto and M. Viana, Positive Lyapunov exponents for Lorenz-like maps with criticalities, these proceedings. | Zbl 0944.37025

[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. | Article | MR 1459261 | Zbl 0908.58053

[Ly2] M. Lyubich, Almost every real quadratic map is either regular or stochastic, preprint 1997. | MR 1935840 | Zbl 1160.37356

[M1] R. Mañe, Contribution to the stability conjecture, Topology 17 (1978), 383-396. | Article | MR 516217 | Zbl 0405.58035

[M2] R. Mañe, A proof of the ${C}^{1}$ stability conjecture, Publ. Math. I.H.E.S. 66 (1987), 161-210. | Article | EuDML 104026 | Numdam | MR 932138 | Zbl 0678.58022

[MN] M. Martens and T. Nowicki, Invariant measures for Lebesgue typical quadratic maps, these proceedings. | Zbl 0939.37020

[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. | Article | EuDML 78400 | Numdam | MR 1420497 | Zbl 0865.58035

[MorY1] C. Moreira and J.-C. Yoccoz, Stable intersections of regular Cantor sets with large Hausdorff dimensions, preprint 1998. | MR 1865980 | Zbl 1195.37015

[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. | Article | MR 1237897 | Zbl 0815.58016

[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 82447 | Numdam | MR 1476293 | Zbl 0911.58022

[MPu2] C. Morales and E. Pujals, Strange attractors containing a singularity with two positive multipliers, Comm. Math. Phys. 196 (1998), 671-679. | Article | MR 1645220 | Zbl 0921.58039

[MPP1] C. Morales, M. J. Pacifico, and E. Pujals, New strange attractors on the boundary of hyperbolic systems, preprint 1997. | Zbl 0957.37032

[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 1490422 | Zbl 0902.58023

[MPP3] C. Morales, M. J. Pacifico, and E. Pujals, Singular hyperbolic sets, Proc. Amer. Math. Soc. 127 (1999), 3343-3400. | MR 1610761 | Zbl 0924.58068

[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 1649489 | Zbl 0918.58036

[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. | Article | EuDML 103959 | Numdam | MR 556584 | Zbl 0445.58022

[PRV1] M. J. Pacifico, A. Rovella, and M. Viana, Infinite-modal maps with global chaotic behavior, Annals of Math. 148 (1998), 441-484. | Article | MR 1668551 | Zbl 0916.58029

[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 120908 | Zbl 0959.37040

[PSh] C. Pugh and M. Shub, Stable ergodicity and julienne quasi-conformality, preprint 1997. | MR 1750453 | Zbl 0964.37017

[PT] J. Palis and F. Takens, Hyperbolicity and sensitive-chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. | MR 1237641 | Zbl 0790.58014

[PT1] J. Palis and F. Takens, Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms, Inventiones Math. 82 (1985), 397-422. | Article | EuDML 143292 | MR 811543 | Zbl 0579.58005

[PT2] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math. 125 (1987), 337-374. | Article | MR 881272 | Zbl 0641.58029

[PV] J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many periodic attractors, Annals of Math. 140 (1994), 207-250. | Article | MR 1289496 | Zbl 0817.58004

[PY1] J. Palis and J.-C. Yoccoz, Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension, Acta Mathematica, vol. 172 (1994), 91-136. | Article | MR 1263999 | Zbl 0801.58035

[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. | Article | MR 1254985 | Zbl 0797.58051

[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. | Article | MR 860314 | Zbl 0602.58036

[U] R. Ures, On the approximation of Hénon-like attractors by homoclinic tangencies, Ergodic Theory and Dynamical Systems, vol. 15 (1995), 1223-1230. | Article | MR 1366318 | Zbl 0841.58044

[V1] M. Viana, Multidimensional nonhyperbolic attractors, Publ. Math. IHES (1997). | EuDML 104121 | MR 1471866 | Zbl 1037.37016

[V2] M. Viana, Dynamics: a probabilistic and geometric perspective, Procs. International Congress of Mathematicians, ICM98-Berlin. | Zbl 0911.58013