Open questions leading to a global perspective in dynamics

Nonlinearity

Volumn 21, Issue 4, 2008, Pages

  Palis, J ^a  

^a IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43049119665     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/4/T01     Document Type: Article

References (22)

1. vila A, de Melo W and Lyubich M 2003 Regular or stochastic dynamics in real analytic families of unimodal maps Inventiones Math. 154 451-550
2. vila A and Moreira C G 2005 Phase-parameter relation and sharp statistical properties for general families of unimodal maps Contemp. Math. 389 1-42 (Preprint: math/0306156v1)
3. vila A and Moreira C G 2005 Statistical properties of unimodal maps: the quadratic family Ann. Math. 161 831-81 (Preprint: math/0010062v5)
4. vila A and Moreira C G 2003 Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative Astérisque 286 81-118 (Preprint: math/0105221v3)
5. Arroyo A and Rodriguez Hertz F 2003 Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows Ann. Inst. H. Poincaré -Anal. Non Linéaire 20 805-41
6. Bonatti C, Diaz L J and Viana M 2004 Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective (Berlin: Springer)
7. Crovisier S Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems Preprint math.DS/0605387 v1 at press
8. Crovisier S and Pujals E R Homoclinic bifurcations versus hyperbolicity in preparation
9. Gorodetski A and Kaloshin V 2007 How often surface diffeomorphism have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency Adv. Math. 208 710-97
10. Kozlovski O, Shen W and van Strien S 2007 Density of hyperbolicity in dimension one Ann. Math. 166 145-82
11. Leal B High dimension diffeomorphisms exhibiting infinitely many strange attractors Ann. Inst. H. Poincaré-Anal. Non Linéaire at press (accessible online via ScienceDirect)
12. Lyubich M 2002 Almost every real quadratic map is either regular or stochastic Ann. Math. 156 1-78
13. Morales C, Pacifico M J and Pujals E R 2003 Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers Ann. Math. 160 375-432
14. Moreira C G T A, Palis J and Viana M 2001 Homoclinic tangencies and fractal invariants in arbitrary dimension C. R. Acad. Sci. Paris 333 475-80
15. Palis J 2000 A global view of dynamics and a conjecture on the denseness of finitude of attractors Astérisque 261 335-47
16. Palis J 2005 A global perspective for non-conservative dynamics Ann. Inst. H. Poincaré-Anal. Non Linéaire 22 485-507
17. Palis J and Viana M 1994 High dimension diffeomorphisms displaying infinitely many sinks Ann. Math. 140 207-50
18. Palis J and Yoccoz J C 2001 Nonuniformily hyperbolic horseshoes unleashed by homoclinic bifurcations and zero density of attractors C. R. Acad. Sci. Paris 333 1-5
19. Pujals E R and Sambarino M 2000 Homoclinic tangencies and hyperbolicity for surface diffeomorphisms Ann. Math. 151 961-1023
20. Tsujii M 2005 Physical measures for partially hyperbolic surface endomorphisms Acta Math. 194 37-132
21. Viana M 1993 Strange attractors in higher dimensions Bull. Braz. Math. Soc. 24 13-62
22. Wen L 2000 Homoclinic tangencies and dominated splittings Nonlinearity 15 1445-69