Volume 11, issue 4 (2011)

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

Volume 22
Issue 8, 3533–4008
Issue 7, 3059–3532
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The entropy efficiency of point-push mapping classes on the punctured disk

Philip Boyland and Jason Harrington

Algebraic & Geometric Topology 11 (2011) 2265–2296
Bibliography
1 G Band, P Boyland, The Burau estimate for the entropy of a braid, Algebr. Geom. Topol. 7 (2007) 1345 MR2350285
2 M Bestvina, M Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995) 109 MR1308491
3 B J Binder, Ghost rods adopting the role of withdrawn baffles in batch mixer designs, Phys. Letters A 374 (2010) 3483
4 J S Birman, Braids, links, and mapping class groups, Annals of Math. Studies 82, Princeton Univ. Press (1974) MR0375281
5 P Boyland, Isotopy stability of dynamics on surfaces, from: "Geometry and topology in dynamics (Winston-Salem, NC, 1998/San Antonio, TX, 1999)" (editors M Barge, K Kuperberg), Contemp. Math. 246, Amer. Math. Soc. (1999) 17 MR1732369
6 P Boyland, Dynamics of two-dimensional time-periodic Euler fluid flows, Topology Appl. 152 (2005) 87 MR2160808
7 P Boyland, H Aref, M A Stremler, Topological fluid mechanics of stirring, J. Fluid Mech. 403 (2000) 277 MR1742169
8 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
9 S Dowdall, Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms arXiv:1004.3936
10 B Farb, C Leininger, D Margalit, Small dilatation pseudo-anosovs and $3$–manifolds arXiv:0905.0219v1
11 B Farb, D Margalit, A primer on mapping class groups, Princeton Math. Ser. 49, Princeton Univ. Press (2011) 488
12 A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
13 M D Finn, S M Cox, H M Byrne, Mixing measures for a two-dimensional chaotic Stokes flow, J. Engrg. Math. 48 (2004) 129 MR2033473
14 M D Finn, J L Thiffeault, Topological optimisation of rod-stirring devices, to appear in SIAM Review arXiv:1004.0639v1
15 D Fried, Periodic points and twisted coefficients, from: "Geometric dynamics (Rio de Janeiro, 1981)" (editor J Pallis), Lecture Notes in Math. 1007, Springer (1983) 261 MR730272
16 D Fried, Entropy and twisted cohomology, Topology 25 (1986) 455 MR862432
17 E Ghate, E Hironaka, The arithmetic and geometry of Salem numbers, Bull. Amer. Math. Soc. $($N.S.$)$ 38 (2001) 293 MR1824892
18 T Hall, Software to compute train tracks of surface homeomorphisms (2005)
19 M Handel, Global shadowing of pseudo-Anosov homeomorphisms, Ergodic Theory Dynam. Systems 5 (1985) 373 MR805836
20 E Hironaka, E Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006) 699 MR2240913
21 R Jungers, The joint spectral radius: Theory and applications, Lecture Notes in Control and Information Sci. 385, Springer (2009) MR2507938
22 T Kobayashi, S Umeda, A design for pseudo-Anosov braids using hypotrochoid curves, Topology Appl. 157 (2010) 280 MR2556106
23 I Kra, On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981) 231 MR611385
24 E Lanneau, J L Thiffeault, On the minimum dilatation of pseudo-anosov homeomorphisms on surfaces of small genus (2011)
25 A Manning, Topological entropy and the first homology group, from: "Dynamical systems—Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E C Zeeman on his fiftieth birthday)" (editor A Manning), Lecture Notes in Math. 468, Springer (1975) 185 MR0650661
26 J O Moussafir, On computing the entropy of braids, Funct. Anal. Other Math. 1 (2006) 37 MR2381961
27 R C Penner, J L Harer, Combinatorics of train tracks, Annals of Math. Studies 125, Princeton Univ. Press (1992) MR1144770
28 J L Thiffeault, M D Finn, Topology, braids and mixing in fluids, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 364 (2006) 3251 MR2317905
29 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. $($N.S.$)$ 19 (1988) 417 MR956596