@incollection{AST_2000__261__335_0, 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}, year = {2000}, mrnumber = {1755446}, zbl = {1044.37014}, language = {en}, url = {http://www.numdam.org/item/AST_2000__261__335_0/} }
TY - CHAP AU - Palis, Jacob TI - A global view of dynamics and a conjecture on the denseness of finitude of attractors BT - Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995 AU - Collectif ED - Flexor Marguerite ED - Sentenac Pierrette ED - Yoccoz Jean-Christophe T3 - Astérisque PY - 2000 SP - 335 EP - 347 IS - 261 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2000__261__335_0/ LA - en ID - AST_2000__261__335_0 ER -
%0 Book Section %A Palis, Jacob %T A global view of dynamics and a conjecture on the denseness of finitude of attractors %B Géométrie complexe et systèmes dynamiques - Colloque en l'honneur d'Adrien Douady Orsay, 1995 %A Collectif %E Flexor Marguerite %E Sentenac Pierrette %E Yoccoz Jean-Christophe %S Astérisque %D 2000 %P 335-347 %N 261 %I Société mathématique de France %U http://www.numdam.org/item/AST_2000__261__335_0/ %G en %F AST_2000__261__335_0
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), pp. 335-347. http://www.numdam.org/item/AST_2000__261__335_0/
[ABV] measures for partially hyperbolic systems: the expanding case, to appear in Invent. Math. | MR | Zbl
, and ,[A] SRB measures for nonhyperbolic systems with multidimensional expansion, thesis IMPA, 1997, to appear in Ann. Sci. ENS. | Numdam | Zbl
,[Ar] On the mapping of the circle into itself, Izvestia Akad. Nauk., USSR Math. Series bf 25 (1961), 21-86. | MR
,[BC] The dynamics of the Hénon maps, Ann. of Math. 133 (1991), 73-169. | DOI | MR | Zbl
and ,[BV1] Solution of the basin problem for Hénon-like attractors, preprint 1999. | MR | Zbl
and ,[BV2] Stochastic stability and other statistical properties for Hénon-like maps, in preparation.
and ,[BY1] Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps, Ergod. Th. & Dynam. Sys. 12 (1992), 13-37. | DOI | MR | Zbl
and ,[BY2] -measures for certain Hénon maps, Invent. Math. 112 (1993), 541-576. | DOI | EuDML | MR | Zbl
and ,[BD] Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math. 143 (1996), 357-396. | DOI | MR | Zbl
and ,[BPV] Lorenz attractors with arbitrary expanding dimension, CR. Acad. Sci. Paris 325 (1997), 883-888. | MR | Zbl
, , and ,[C] Infinitely many coexisting strange attractors, to appear, Annales de l'Inst. Henri Poincaré, 15 (1998), 539-579. | DOI | EuDML | Numdam | MR | Zbl
,[C] Infinitely many coexisting strange attractors, to appear, Analyse Non linéaire 15 (1998), 539-579. | DOI | EuDML | Numdam | MR | Zbl
,[CE1] Homoclinic tangencies near cascades of period doubling bifurcations, to appear, Ann. de l'Inst. Henri Poincaré Analyse Nonlinéaire. | EuDML | Numdam | MR | Zbl
and ,[CE2] Persistence of the Feigenbaum attractor in oneparameter families, preprint 1997. | MR | Zbl
and ,[CT] Iterations d'endomorphismes et groupe de renormalisation, CRAS Paris 287 (1978), 577-580. | MR | Zbl
and ,[dMM] Universal models for Lorenz maps, preprint 1997, to appear, Ergodic Th. and Dyn. Syst. | MR | Zbl
and ,[dM] Rigidity and renormalization in one-dimensional dynamics, Procs. International Congress of Mathematicians, ICM98-Berlin. | Zbl
,[dMS] One-dimensional dynamics, Springer-Verlag, 1993. | MR | Zbl
and ,[DRV] Strange attractors in saddle-node cycles: prevalence and globality, Invent. Math. 125 (1996), 37-74. | DOI | MR | Zbl
, , and ,[DPU] Normal hyperbolicity and robust transitivity, preprint 1997, to appear in Acta Math. | MR | Zbl
, , and ,[F] Quantitative universality for a class of nonlinear transformations, J. Stat. Phys. 19 (1978), 25-52. | DOI | MR | Zbl
,[GS] Generic hyperbolicity in the logistic family, Annals of Math. 146 (1997), 1-52. | DOI | MR | Zbl
and ,[Ha] Connecting invariant manifolds and the solution of the stability and -stability conjectures for flows, Annals of Math. 145 (1997), 81-137. | DOI | MR | Zbl
,[He] A two dimensional mapping with a strange attractor, Comm. Math. Phys. 50 (1976), 69-77. | DOI | MR | Zbl
,[H] Sur la conjugaison différentiable des difféomorphims du cercle à des rotations, Publ. Math. 49 (1979), 5-233. | DOI | EuDML | Numdam | MR | Zbl
.[J] Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. | DOI | MR | Zbl
,[K] Random perturbations of dynamical systems, Birkhäuser, 1988. | DOI | MR | Zbl
,[Ko] Structural stability in one-dimensional dynamics, PhD thesis, Univ. Amsterdam, 1997.
,[L] Deterministic nonperiodic flow, J. Atmosph. Sci. 20 (1963), 130-141. | DOI | Zbl
,[LP] Stability of singular horseshoes, Topology 25 (1986), 337-352. | DOI | MR | Zbl
and ,[LV1] Positive Lyapunov exponents for Lorenz-like maps with criticalities, these proceedings. | Numdam | Zbl
and ,[LV2] Lorenz-like attractors without invariant foliations, in preparation.
and ,[Ly1] Dynamics of quadratic polynomials I-II, Acta Math., 178 (1997), 185-297. | DOI | MR | Zbl
,[Ly2] Almost every real quadratic map is either regular or stochastic, preprint 1997. | MR | Zbl
,[M1] Contribution to the stability conjecture, Topology 17 (1978), 383-396. | DOI | MR | Zbl
,[M2] A proof of the stability conjecture, Publ. Math. I.H.E.S. 66 (1987), 161-210. | DOI | EuDML | Numdam | MR | Zbl
,[MN] Invariant measures for Lebesgue typical quadratic maps, these proceedings.
and ,[Mor] 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] Stable intersections of regular Cantor sets with large Hausdorff dimensions, preprint 1998. | MR | Zbl
and ,[MorY2] Stable homoclinic tangencies for hyperbolic sets of large Hausdorff dimension, in preparation.
and ,[MV] Abundance of strange attractors, Acta Math. 171 (1993), 1-71. | DOI | MR | Zbl
and ,[MPa] New singular strange attractors arising from hyperbolic systems, preprint 1997.
and ,[MPu1] Singular strange attractors on the boundary of Morse-Smale systems, Ann. Sci. E.N.S. 30 (1997), 693-718. | EuDML | Numdam | MR | Zbl
and ,[MPu2] Strange attractors containing a singularity with two positive multipliers, Comm. Math. Phys. 196 (1998), 671-679. | DOI | MR | Zbl
and ,[MPP1] New strange attractors on the boundary of hyperbolic systems, preprint 1997. | Zbl
, , and ,[MPP2] Global attractors from the explosion of singular cycles, CR. Acad. Sci. Paris 325 (1997), 1317-1322. | MR | Zbl
, , and ,[MPP3] Singular hyperbolic sets, Proc. Amer. Math. Soc. 127 (1999), 3343-3400. | MR | Zbl
, , and ,[MPP4] On robust singular transitive sets for three-dimensional flows, CR. Acad. Sci. Paris 326 (1998), 81-86. | MR | Zbl
, , and ,[N] 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] Infinite-modal maps with global chaotic behavior, Annals of Math. 148 (1998), 441-484. | DOI | MR | Zbl
, , and ,[PRV2] Persistence of global spiraling attractors, in preparation.
, , and ,[PS] Homoclinic tangencies and hyperbolicity for surface diffeomorphisms: A conjecture of Palis, preprint 1998, to appear in Annals of Math. | EuDML | Zbl
and ,[PSh] Stable ergodicity and julienne quasi-conformality, preprint 1997. | MR | Zbl
and ,[PT] Hyperbolicity and sensitive-chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. | MR | Zbl
and ,[PT1] Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms, Inventiones Math. 82 (1985), 397-422. | DOI | EuDML | MR | Zbl
and ,[PT2] Hyperbolicity and the creation of homoclinic orbits, Annals of Math. 125 (1987), 337-374. | DOI | MR | Zbl
and ,[PV] High dimension diffeomorphisms displaying infinitely many periodic attractors, Annals of Math. 140 (1994), 207-250. | DOI | MR | Zbl
and ,[PY1] Homoclinic tangencies for hyperbolic sets of large Hausdorff dimension, Acta Mathematica, vol. 172 (1994), 91-136. | DOI | MR | Zbl
and ,[PY2] Non-uniform hyperbolic horseshoes arising from homoclinic bifurcations, to appear in CR. Acad. Sci. Paris.
and ,[R] The dynamics of perturbations of the contracting Lorenz attractor, Bull. Braz. Math. Soc. vol. 24, n° 2 (1993), 233-259. | DOI | MR | Zbl
,[S] Topological transitive diffeomorphisms on ^, Lecture Notes in Math. 206 (1971), 39, Springer-Verlag.
,[TY] How often do simple dynamical processes have infinitely many coexisting sinks? Comm. Math. Phys. 106 (1986), 635-657. | DOI | MR | Zbl
and ,[U] On the approximation of Hénon-like attractors by homoclinic tangencies, Ergodic Theory and Dynamical Systems, vol. 15 (1995), 1223-1230. | DOI | MR | Zbl
,[V1] Multidimensional nonhyperbolic attractors, Publ. Math. IHES (1997). | EuDML | MR | Zbl
,[V2] Dynamics: a probabilistic and geometric perspective, Procs. International Congress of Mathematicians, ICM98-Berlin. | Zbl
,