A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov's coordinates on the boundary of Teichmüller space, is described. The method is illustrated on two twoparameter families of braids.2000 Mathematics Subject Classification. 37E30, 37B40.
We compare the spectra of Dynnikov matrices with the spectra of the train track transition matrices of a given pseudo-Anosov braid on the finitely punctured disk, and show that these matrices are isospectral up to roots of unity and zeros under some particular conditions. It is shown, via examples, that Dynnikov matrices are much easier to compute than transition matrices, and so yield data that was previously inaccessible.
We give a recipe to compute the geometric intersection number of an integral lamination with a particular type of integral lamination on an n-times punctured disk. This provides a way to find the geometric intersection number of two arbitrary integral laminations when combined with an algorithm of Dynnikov and Wiest.2010 Mathematics Subject Classification. 57N16, 57N37,57N05.
We present an algorithm for calculating the geometric intersection number of two multicurves on the n-punctured disk, taking as input their Dynnikov coordinates.The algorithm has complexity O(m 2 n 4 ), where m is the sum of the absolute values of the Dynnikov coordinates of the two multicurves. The main ingredient is an algorithm due to Cumplido for relaxing a multicurve.
We present an efficient algorithm for calculating the number of components of an integral lamination on an n-punctured disk, given its Dynnikov coordinates.The algorithm requires O(n 2 M ) arithmetic operations, where M is the sum of the absolute values of the Dynnikov coordinates.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.