Volume 22, issue 4 (2018)

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

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

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 Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Rotation intervals and entropy on attracting annular continua

Alejandro Passeggi, Rafael Potrie and Martín Sambarino

Geometry & Topology 22 (2018) 2145–2186
Bibliography
1 R H Abraham, H B Stewart, A chaotic blue sky catastrophe in forced relaxation oscillations, Phys. D 21 (1986) 394 MR862266
2 M U Akhmet, M O Fen, Entrainment by chaos, J. Nonlinear Sci. 24 (2014) 411 MR3215082
3 L Alsedà, J Llibre, F Mañosas, M Misiurewicz, Lower bounds of the topological entropy for continuous maps of the circle of degree one, Nonlinearity 1 (1988) 463 MR955624
4 M C Arnaud, C Bonatti, S Crovisier, Dynamiques symplectiques génériques, Ergodic Theory Dynam. Systems 25 (2005) 1401 MR2173426
5 M Barge, R M Gillette, Rotation and periodicity in plane separating continua, Ergodic Theory Dynam. Systems 11 (1991) 619 MR1145613
6 F Beguín, Ensembles de rotations des homéomorphismes du tore 𝕋2, lecture notes (2007)
7 G D Birkhoff, Sur quelques courbes fermées remarquables, Bull. Soc. Math. France 60 (1932) 1 MR1504983
8 C Bonatti, S Crovisier, Récurrence et généricité, Invent. Math. 158 (2004) 33 MR2090361
9 C Bonatti, L J Díaz, E R Pujals, A C1–generic dichotomy for diffeomorphisms : weak forms of hyperbolicity or infinitely many sinks or sources, Ann. of Math. 158 (2003) 355 MR2018925
10 J P Boroński, P Oprocha, Rotational chaos and strange attractors on the 2–torus, Math. Z. 279 (2015) 689 MR3318245
11 H W Broer, KAM theory : the legacy of A N Kolmogorov’s 1954 paper, Bull. Amer. Math. Soc. 41 (2004) 507 MR2083638
12 A Chenciner, Poincaré and the three-body problem, from: "Henri Poincaré, 1912–2012" (editors B Duplantier, V Rivasseau), Prog. Math. Phys. 67, Springer (2015) 51 MR3329413
13 S Crovisier, Perturbation of C1–diffeomorphisms and generic conservative dynamics on surfaces, from: "Dynamique des difféomorphismes conservatifs des surfaces : un point de vue topologique", Panor. Synthèses 21, Soc. Math. France (2006) 1 MR2288283
14 J Franks, Necessary conditions for stability of diffeomorphisms, Trans. Amer. Math. Soc. 158 (1971) 301 MR0283812
15 J Franks, Rotation vectors for surface diffeomorphisms, from: "Proceedings of the International Congress of Mathematicians" (editor S D Chatterji), Birkhäuser (1995) 1179 MR1404018
16 J Franks, M Handel, Entropy zero area preserving diffeomorphisms of S2, Geom. Topol. 16 (2012) 2187 MR3033517
17 J Franks, P Le Calvez, Regions of instability for non-twist maps, Ergodic Theory Dynam. Systems 23 (2003) 111 MR1971199
18 M Girard, Sur les courbes invariantes par un difféomorphisme C1–générique symplectique d’une surface, PhD thesis, Université d’Avignon (2009)
19 J G Hocking, G S Young, Topology, Addison-Wesley (1961) MR0125557
20 T Jäger, Linearization of conservative toral homeomorphisms, Invent. Math. 176 (2009) 601 MR2501297
21 T Jäger, A Passeggi, On torus homeomorphisms semiconjugate to irrational rotations, Ergodic Theory Dynam. Systems 35 (2015) 2114 MR3394110
22 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
23 J Kennedy, J A Yorke, Topological horseshoes, Trans. Amer. Math. Soc. 353 (2001) 2513 MR1707195
24 A Koropecki, Realizing rotation numbers on annular continua, Math. Z. 285 (2017) 549 MR3598824
25 A Koropecki, P Le Calvez, M Nassiri, Prime ends rotation numbers and periodic points, Duke Math. J. 164 (2015) 403 MR3314477
26 A Koropecki, A Passeggi, A Poincaré–Bendixson theorem for translation lines and applications to prime ends, preprint (2017) arXiv:1701.04644
27 J M Kwapisz, Rotation sets and entropy, PhD thesis, State University of New York at Stony Brook (1995) MR2693427
28 P Le Calvez, Propriétés des attracteurs de Birkhoff, Ergodic Theory Dynam. Systems 8 (1988) 241 MR951271
29 P Le Calvez, Une version feuilletée équivariante du théorème de translation de Brouwer, Publ. Math. Inst. Hautes Études Sci. 102 (2005) 1 MR2217051
30 P Le Calvez, F A Tal, Forcing theory for transverse trajectories of surface homeomorphisms, preprint (2015) arXiv:1503.09127
31 J Llibre, R S MacKay, Rotation vectors and entropy for homeomorphisms of the torus isotopic to the identity, Ergodic Theory Dynam. Systems 11 (1991) 115 MR1101087
32 J N Mather, Topological proofs of some purely topological consequences of Carathéodory’s theory of prime ends, from: "Selected studies: physics-astrophysics, mathematics, history of science" (editors T M Rassias, G M Rassias), North-Holland (1982) 225 MR662863
33 S Matsumoto, Prime end rotation numbers of invariant separating continua of annular homeomorphisms, Proc. Amer. Math. Soc. 140 (2012) 839 MR2869068
34 J W Milnor, Attractor, Scholarpedia 1 (2006)
35 M Misiurewicz, K Ziemian, Rotation sets for maps of tori, J. London Math. Soc. 40 (1989) 490 MR1053617
36 M H A Newman, Elements of the topology of plane sets of points, Cambridge Univ. Press (1951) MR0044820
37 A Passeggi, Contributions in surface dynamics: a classification of minimal sets of homeomorphisms and aspects of the rotation theory on the torus, PhD thesis, Friedrich-Alexander-Universität, Erlangen (2013)
38 A Passeggi, J Xavier, A classification of minimal sets for surface homeomorphisms, Math. Z. 278 (2014) 1153 MR3278909
39 R Shaw, Strange attractors, chaotic behavior, and information flow, Z. Naturforsch. A 36 (1981) 80 MR604920
40 M Shub, All, most, some differentiable dynamical systems, from: "Proceedings of the International Congress of Mathematicians" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 99 MR2275672
41 J M T Thompson, H B Stewart, Nonlinear dynamics and chaos, Wiley (2002) MR1963884
42 R B Walker, Periodicity and decomposability of basin boundaries with irrational maps on prime ends, Trans. Amer. Math. Soc. 324 (1991) 303 MR992609