On the topological entropy of families of braids

Topology and its Applications

Volumn 156, Issue 8, 2009, Pages 1554-1564

  Hall, Toby ^a   Yurttaş, S Öykü ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Dynnikov coordinates; Nielsen Thurston classification; Topological entropy

Indexed keywords

EID: 62049085583     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2009.01.005     Document Type: Article

References (13)

1. Bestvina M., and Handel M. Train-tracks for surface homeomorphisms. Topology 34 1 (1995) 109-140
2. Birman J. Braids, Links, and Mapping Class Groups. Ann. of Math. Stud. vol. 82 (1974), Princeton University Press, Princeton, NJ
3. Boyland P. Isotopy stability of dynamics on surfaces. Geometry and Topology in Dynamics. Winston-Salem, NC, 1998/San Antonio, TX, 1999. Contemp. Math. vol. 246 (1999), Amer. Math. Soc., Providence, RI 17-45
4. Dehornoy P. Efficient solutions to the braid isotopy problem. arXiv:math/0703666
5. Dehornoy P., Dynnikov I., Rolfsen D., and Wiest B. Why are Braids Orderable?. Panor. Syntheses vol. 14 (2002), Soc. Math. France, Paris
6. Dynnikov I.A. On a Yang-Baxter mapping and the Dehornoy ordering. Uspekhi Mat. Nauk 57 3(345) (2002) 151-152
7. Fathi A., Laudenbach F., and Poénaru V. Travaux de Thurston sur les surfaces (1979), Soc. Math. France, Paris Séminaire Orsay
8. Finn M., and Thiffeault J.-L. Topological entropy of braids on the torus. SIAM J. Appl. Dyn. Syst. 6 1 (2007) 79-98 (electronic)
9. Franks J., and Misiurewicz M. Cycles for disk homeomorphisms and thick trees. Nielsen Theory and Dynamical Systems. South Hadley, MA, 1992 (1993), Amer. Math. Soc., Providence, RI 69-139
10. Hironaka E., and Kin E. A family of pseudo-Anosov braids with small dilatation. Algebr. Geom. Topol. 6 (2006) 699-738 (electronic)
11. Los J. Pseudo-Anosov maps and invariant train tracks in the disc: A finite algorithm. Proc. London Math. Soc. (3) 66 2 (1993) 400-430
12. Moussafir J.-O. On computing the entropy of braids. Funct. Anal. Other Math. 1 1 (2006) 37-46
13. Thurston W. On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.) 19 2 (1988) 417-431