TY - JOUR AU - Anušić, Ana AU - Mouron, Christopher PY - 2022/06/12 Y2 - 2024/03/29 TI - Topological entropy of diagonal maps on inverse limit spaces JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 59 IS - 2B SE - DO - 10.12775/TMNA.2021.043 UR - https://apcz.umk.pl/TMNA/article/view/38705 SP - 867 - 895 AB - 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 $\max\{\mbox{\rm Ent}(f),\mbox{\rm Ent}(g)\}$. As a side product, we develop some techniques for computing topological entropy of set-valued maps. ER -