Volume 20, issue 6 (2016)

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

Volume 24, 1 issue

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
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Cylindrical contact homology and topological entropy

Marcelo R R Alves

Geometry & Topology 20 (2016) 3519–3569
Bibliography
1 P Albers, B Bramham, C Wendl, On nonseparating contact hypersurfaces in symplectic 4–manifolds, Algebr. Geom. Topol. 10 (2010) 697 MR2606798
2 M R R Alves, Growth rate of Legendrian contact homology and dynamics of Reeb flows, PhD thesis, Université Libre de Bruxelles (2014)
3 M R R Alves, Legendrian contact homology and topological entropy, preprint (2014) arXiv:1410.3381
4 M R R Alves, Positive topological entropy for Reeb flows on 3–dimensional Anosov contact manifolds, preprint (2015) arXiv:1512.03140
5 M R R Alves, P A S Salomão, Legendrian contact homology on the complement of Reeb orbits and topological entropy, in preparation
6 F Bourgeois, A survey of contact homology, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 45 MR2555933
7 F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
8 F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
9 F Bourgeois, K Mohnke, Coherent orientations in symplectic field theory, Math. Z. 248 (2004) 123 MR2092725
10 R Bowen, Topological entropy and axiom A, from: "Global Analysis" (editors S S Chern, S Smale), Amer. Math. Soc. (1970) 23 MR0262459
11 P Boyland, Isotopy stability of dynamics on surfaces, from: "Geometry and topology in dynamics" (editors M Barge, K Kuperberg), Contemp. Math. 246, Amer. Math. Soc. (1999) 17 MR1732369
12 V Colin, K Honda, Constructions contrôlées de champs de Reeb et applications, Geom. Topol. 9 (2005) 2193 MR2209370
13 D L Dragnev, Fredholm theory and transversality for noncompact pseudoholomorphic maps in symplectizations, Comm. Pure Appl. Math. 57 (2004) 726 MR2038115
14 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267
15 A Fathi, F Laudenbach, V Poenaru, editors, Travaux de Thurston sur les surfaces, 66, Société Mathématique de France (1979) 284 MR568308
16 A Fel’shtyn, Dynamical zeta functions, Nielsen theory and Reidemeister torsion, 699, Amer. Math. Soc. (2000) MR1697460
17 S R Fenley, Homotopic indivisibility of closed orbits of 3–dimensional Anosov flows, Math. Z. 225 (1997) 289 MR1464932
18 P Foulon, B Hasselblatt, Contact Anosov flows on hyperbolic 3–manifolds, Geom. Topol. 17 (2013) 1225 MR3070525
19 U Frauenfelder, C Labrousse, F Schlenk, Slow volume growth for Reeb flows on spherizations and contact Bott–Samelson theorems, J. Topol. Anal. 7 (2015) 407 MR3346928
20 U Frauenfelder, F Schlenk, Volume growth in the component of the Dehn–Seidel twist, Geom. Funct. Anal. 15 (2005) 809 MR2221151
21 U Frauenfelder, F Schlenk, Fiberwise volume growth via Lagrangian intersections, J. Symplectic Geom. 4 (2006) 117 MR2275001
22 U Frauenfelder, F Schlenk, Filtered Hopf algebras and counting geodesic chords, Math. Ann. 360 (2014) 995 MR3273650
23 D T Gay, Four-dimensional symplectic cobordisms containing three-handles, Geom. Topol. 10 (2006) 1749 MR2284049
24 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
25 M Handel, W P Thurston, Anosov flows on new three manifolds, Invent. Math. 59 (1980) 95 MR577356
26 H Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 515 MR1244912
27 H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectisations, I : Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 337 MR1395676
28 H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectizations, III : Fredholm theory, from: "Topics in nonlinear analysis" (editors J Escher, G Simonett), Progr. Nonlinear Differential Equations Appl. 35, Birkhäuser (1999) 381 MR1725579
29 H Hofer, K Wysocki, E Zehnder, Finite energy foliations of tight three-spheres and Hamiltonian dynamics, Ann. of Math. 157 (2003) 125 MR1954266
30 U Hryniewicz, A Momin, P A S Salomão, A Poincaré–Birkhoff theorem for tight Reeb flows on S3, Invent. Math. 199 (2015) 333 MR3302117
31 B Jiang, Estimation of the number of periodic orbits, Pacific J. Math. 172 (1996) 151 MR1379291
32 A Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Inst. Hautes Études Sci. Publ. Math. 51 (1980) 137 MR573822
33 A Katok, Entropy and closed geodesics, Ergodic Theory Dynam. Systems 2 (1982) 339 MR721728
34 A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, 54, Cambridge Univ. Press (1995) MR1326374
35 Y Lima, O Sarig, Symbolic dynamics for three-dimensional flows with positive topological entropy, preprint (2014) arXiv:1408.3427
36 L Macarini, F Schlenk, Positive topological entropy of Reeb flows on spherizations, Math. Proc. Cambridge Philos. Soc. 151 (2011) 103 MR2801317
37 A Momin, Contact homology of orbit complements and implied existence, J. Mod. Dyn. 5 (2011) 409
38 G P Paternain, Geodesic flows, 180, Birkhäuser (1999) MR1712465
39 C Robinson, Dynamical systems: Stability, symbolic dynamics, and chaos, CRC Press (1995) MR1396532
40 A Vaugon, On growth rate and contact homology, Algebr. Geom. Topol. 15 (2015) 623 MR3342671
41 C Wendl, Strongly fillable contact manifolds and J–holomorphic foliations, Duke Math. J. 151 (2010) 337 MR2605865