Volume 24, issue 4 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence

Christian Bonatti, Andrey Gogolev, Andy Hammerlindl and Rafael Potrie

Geometry & Topology 24 (2020) 1751–1790
Bibliography
1 T Barbot, Mise en position optimale de tores par rapport à un flot d’Anosov, Comment. Math. Helv. 70 (1995) 113 MR1314942
2 F Béguin, C Bonatti, B Yu, Building Anosov flows on 3–manifolds, Geom. Topol. 21 (2017) 1837 MR3650083
3 C Bonatti, S Crovisier, Récurrence et généricité, Invent. Math. 158 (2004) 33 MR2090361
4 C Bonatti, L J Díaz, Persistent nonhyperbolic transitive diffeomorphisms, Ann. of Math. 143 (1996) 357 MR1381990
5 C Bonatti, L J Díaz, R Ures, Minimality of strong stable and unstable foliations for partially hyperbolic diffeomorphisms, J. Inst. Math. Jussieu 1 (2002) 513 MR1954435
6 C Bonatti, L J Díaz, M Viana, Dynamics beyond uniform hyperbolicity, 102, Springer (2005) MR2105774
7 C Bonatti, J Franks, A Hölder continuous vector field tangent to many foliations, from: "Modern dynamical systems and applications" (editors M Brin, B Hasselblatt, Y Pesin), Cambridge Univ. Press (2004) 299 MR2090776
8 C Bonatti, A Gogolev, R Potrie, Anomalous partially hyperbolic diffeomorphisms, II : Stably ergodic examples, Invent. Math. 206 (2016) 801 MR3573973
9 C Bonatti, N Guelman, Axiom A diffeomorphisms derived from Anosov flows, J. Mod. Dyn. 4 (2010) 1 MR2643887
10 C Bonatti, R Langevin, Un exemple de flot d’Anosov transitif transverse à un tore et non conjugué à une suspension, Ergodic Theory Dynam. Systems 14 (1994) 633 MR1304136
11 C Bonatti, C Matheus, M Viana, A Wilkinson, Abundance of stable ergodicity, Comment. Math. Helv. 79 (2004) 753 MR2099120
12 C Bonatti, K Parwani, R Potrie, Anomalous partially hyperbolic diffeomorphisms, I : Dynamically coherent examples, Ann. Sci. École Norm. Sup. 49 (2016) 1387 MR3592360
13 C Bonatti, A Wilkinson, Transitive partially hyperbolic diffeomorphisms on 3–manifolds, Topology 44 (2005) 475 MR2122214
14 C Bonatti, J Zhang, Transverse foliations on the torus 𝕋2 and partially hyperbolic diffeomorphisms on 3–manifolds, Comment. Math. Helv. 92 (2017) 513 MR3682779
15 M Brin, On dynamical coherence, Ergodic Theory Dynam. Systems 23 (2003) 395 MR1972227
16 M Brin, D Burago, S Ivanov, Dynamical coherence of partially hyperbolic diffeomorphisms of the 3–torus, J. Mod. Dyn. 3 (2009) 1 MR2481329
17 M Brunella, Separating the basic sets of a nontransitive Anosov flow, Bull. Lond. Math. Soc. 25 (1993) 487 MR1233413
18 D Burago, S Ivanov, Partially hyperbolic diffeomorphisms of 3–manifolds with abelian fundamental groups, J. Mod. Dyn. 2 (2008) 541 MR2449138
19 K Burns, A Wilkinson, Dynamical coherence and center bunching, Discrete Contin. Dyn. Syst. 22 (2008) 89 MR2410949
20 D Calegari, Foliations and the geometry of 3–manifolds, Oxford Univ. Press (2007) MR2327361
21 R D Canary, D McCullough, Homotopy equivalences of 3–manifolds and deformation theory of Kleinian groups, 812, Amer. Math. Soc. (2004) MR2096234
22 P D Carrasco, F Rodriguez-Hertz, J Rodriguez-Hertz, R Ures, Partially hyperbolic dynamics in dimension three, Ergodic Theory Dynam. Systems 38 (2018) 2801 MR3868015
23 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, 9, Cambridge Univ. Press (1988) MR964685
24 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
25 A Hammerlindl, R Potrie, Classification of partially hyperbolic diffeomorphisms in 3–manifolds with solvable fundamental group, J. Topol. 8 (2015) 842 MR3394318
26 A Hammerlindl, R Potrie, Partial hyperbolicity and classification: a survey, Ergodic Theory Dynam. Systems 38 (2018) 401 MR3774827
27 A Hammerlindl, R Potrie, M Shannon, Seifert manifolds admitting partially hyperbolic diffeomorphisms, J. Mod. Dyn. 12 (2018) 193 MR3824728
28 M Handel, W P Thurston, New proofs of some results of Nielsen, Adv. Math. 56 (1985) 173 MR788938
29 K Johannson, Homotopy equivalences of 3–manifolds with boundaries, 761, Springer (1979) MR551744
30 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
31 S Matsumoto, Some remarks on foliated S1 bundles, Invent. Math. 90 (1987) 343 MR910205
32 D McCullough, Virtually geometrically finite mapping class groups of 3–manifolds, J. Differential Geom. 33 (1991) 1 MR1085134
33 R T Miller, Geodesic laminations from Nielsen’s viewpoint, Adv. Math. 45 (1982) 189 MR664623
34 R Potrie, A few remarks on partially hyperbolic diffeomorphisms of 𝕋3 isotopic to Anosov, J. Dynam. Differential Equations 26 (2014) 805 MR3274442
35 E R Pujals, M Sambarino, A sufficient condition for robustly minimal foliations, Ergodic Theory Dynam. Systems 26 (2006) 281 MR2201949
36 F Rodriguez Hertz, M A Rodriguez Hertz, A Tahzibi, R Ures, Creation of blenders in the conservative setting, Nonlinearity 23 (2010) 211 MR2578476
37 F Rodriguez Hertz, M A Rodriguez Hertz, R Ures, Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D–center bundle, Invent. Math. 172 (2008) 353 MR2390288
38 F Rodriguez Hertz, M A Rodriguez Hertz, R Ures, A non-dynamically coherent example on 𝕋3, Ann. Inst. H Poincaré Anal. Non Linéaire 33 (2016) 1023 MR3519530
39 Y Shi, Perturbations of partially hyperbolic automorphisms on Heisenberg nilmanifold, PhD thesis, Peking University (2014)
40 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
41 F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR224099
42 A Wilkinson, Conservative partially hyperbolic dynamics, from: "Proceedings of the International Congress of Mathematicians, III" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan (2010) 1816 MR2827868