arXiv subjects

Wolfgang Krieger

Publications and source records attributed to Wolfgang Krieger.

22 records · Page 2Linked to original sources

arXiv2007

Zeta functions and topological entropy of the Markov-Dyck shifts

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, {\it Circular codes, loop counting, and zeta-functions}, J. Combinatorial Theory {\bf 56} (1991), pp. 75--83). For a class of examples that includes the Fibonacci-Dyck shift the zeta functions and topological entropy ae determined.

math.DS↗

arXiv2006

On Lambda-Graph Systems for Subshifts of Subshifts

Kengo Matsumoto has introduced lambda-graph systems and strong shift equivalence of lambda-graph systems [Doc.Math.4 (1999), 285-340]. We associate to a subshift of a subshift a lambda-graph system. The strong shift equivalence class of the associated lambda-graph system is an invariant of subsystem equivalence. Wolfgang Krieger and Kengo Matsumoto have introduced the lambda$-entropy of a lambda-graph system and have shown its invariance under strong shift equivalence [Ergod.Th.&Dynam.Sys. 24 (2004) 1155 - 1172]. A separation entropy of a subshift of a subshift is introduced as the lambda-entropy of the associated lambda-graph system.

math.DS↗

arXiv2006

On a certain class of $g$-functions for subshifts

A property $(D)$ of subshifts was defined in: Wolfgang Krieger, On $g$-functions for subshifts, IMS Lecture Notes- Monograph Series, Vol. 48, Dynamics & Stochastics (2006) 306 - 316, arXiv:math.DS/0608259. With a view towards a theory of $g$-fnctions beyond the case of finte type subshifts partially defined continuous $g$-functions of property $(D)$ subshifts are studied.

math.DS↗

arXiv2006

On $g$-functions for subshifts

A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous $g$-function.

math.DS↗