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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