Abstract
We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal component is the same map $g\colon I\to I$ which strongly commutes with $f$ (i.e. $f^{-1}\circ g=g\circ f^{-1}$), we show that the entropy equals $\max\{{\rm Ent}(f),{\rm Ent}(g)\}$. As a side product, we develop some techniques for computing topological entropy of set-valued maps.
Citation
Ana Anušić. Christopher Mouron. "Topological entropy of diagonal maps on inverse limit spaces." Topol. Methods Nonlinear Anal. 59 (2B) 867 - 895, 2022. https://doi.org/10.12775/TMNA.2021.043
Information