Calculating topological entropy
This paper deals with the attempt to find effective algorithms for calculating the topological entropy of piecewise monotone maps of the interval having more than three pieces. The original motivation for the algorithms described in this paper is based on the following fact: If \(g\) is a piecewise monotone continuous function on the unit interval, then \(h(g)= \lim_{n\to \infty} \frac 1n \log \operatorname {Var}(g^n)\), where \(h(g)\) denotes the topological entropy of \(g\), and Var denotes the total variation. The authors present a modified algorithm based on the above mentioned result and prove that this algorithm is equivalent to the standard power method for finding eigenvalues of matrices (with shift of origin) in those cases for which the function is Markov. The authors present the numerical results when this algorithm is applied to a number of examples.
scientific article; zbMATH DE number 1279504