Polynomial entropy for interval maps and lap number
The concept of polynomial entropy was introduced by \textit{J.-P. Marco} [Regul. Chaotic Dyn. 18, No. 6, 623--655 (2013; Zbl 1286.70022)]. Here the authors obtain two upper bounds on the polynomial entropy for piecewise monotone interval maps using the number of monotone pieces of iterates of the maps (lap number) and the total variation of the iterates. The authors also present a lower bound for the polynomial entropy which holds if the preimages of the set of turning points does not accumulate on the set of turning points.
scientific article; zbMATH DE number 7345484
scientific article