Moussafir, Jacques-Olivier On computing the entropy of braids. (English) Zbl 1149.37302 Funct. Anal. Other Math. 1, No. 1, 37-46 (2006). Summary: We consider the problem of computing the entropy of a braid. We recall its definition and for each braid construct a sequence of real numbers whose limit is the braid’s entropy. We state one conjecture on the convergence speed and two conjectures on braids that have high entropy but are written with few letters. Cited in 12 Documents MSC: 37B40 Topological entropy 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 57M07 Topological methods in group theory Keywords:braid; topological entropy; pseudo-Anosov map; lamination; train tracks; surface diffeomorphisms Software:NTL PDFBibTeX XMLCite \textit{J.-O. Moussafir}, Funct. Anal. Other Math. 1, No. 1, 37--46 (2006; Zbl 1149.37302) Full Text: DOI arXiv References: [1] Boyland P (1994) Topological methods in surface dynamics. Topology Appl 58(3):223–298 · Zbl 0810.54031 · doi:10.1016/0166-8641(94)00147-2 [2] Fathi A, Laudenbach F, Poenaru V (1991) Travaux de Thurston sur les surfaces. Séminaire Orsay, 2nd edn, Astérisque, vols 66, 67. Centre National de la Recherche Scientifique [3] Bestvina M, Handel M (1995) Train-tracks for surface homeomorphisms. Topology 34(1):109–140 · Zbl 0837.57010 · doi:10.1016/0040-9383(94)E0009-9 [4] Dynnikov IA, Wiest B (2004) On the complexity of braids. http://hal.ccsd.cnrs.fr/ . Cited 26 May 2006 · Zbl 1187.20045 [5] Katok A, Hasselblatt B (1995) Introduction to the modern theory of dynamical systems. Cambridge Univ Press, Cambridge · Zbl 0878.58020 [6] Dynnikov IA (2002) On a Yang-Baxter mapping and the Dehornoy ordering. Russ Math Surveys 57(3):592–594 · Zbl 1067.20501 · doi:10.1070/RM2002v057n03ABEH000519 [7] Birman JS (1974) Braids, links, and mapping class groups. Princeton Univ Press, Princeton [8] Shoup V (2001) Ntl: a library for doing number theory. http://www.shoup.net . Cited 26 May 2006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.