Volume 11, issue 4 (2011)

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

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

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3 B J Binder, Ghost rods adopting the role of withdrawn baffles in batch mixer designs, Phys.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