Let f be an orientation-preserving homeomorphism of the disk D, P a finite invariant subset and [fP ] the isotopy class of f in D \ P . We give a non trivial lower bound of the topological entropy for maps in [fP ], using the spectral radius of some specializations in GL(n,C) of the Burau matrix associated with [fP ] and we discuss some examples.

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

Abstract We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincare surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show...

A word is quasiperiodic (or coverable) if it can be covered with occurrences of another finite word, called its quasiperiod. A word is multi-scale quasiperiodic (or multi-scale coverable) if it has infinitely many different quasiperiods. These notions were previously studied in the domains of text algorithms and combinatorics of right infinite words. We extend them to infinite pictures (two-dim...

It is known that the topological entropy for the geodesic flow on a Riemannian manifoldM is bounded if the absolute value of sectional curvature |KM | is bounded. We replace this condition by the condition of Ricci curvature and injectivity radius.

The Markov-Dyck shifts arise from finite directed graphs. An expression for the zeta function of a Markov-Dyck shift is given. The derivation of this expression is based on a formula in Keller (G. Keller, Circular codes, loop counting, and zeta-functions, J. Combinatorial Theory 56 (1991), pp. 75– 83). For a class of examples that includes the Fibonacci-Dyck shift the zeta functions and topolog...

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.