Topological entropy of diagonal maps on inverse limit spaces
DOI:
https://doi.org/10.12775/TMNA.2021.043Keywords
Topological entropy, inverse limit space, set-valued mapsAbstract
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.References
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