Let $m\in\mathbb{N}$ such that $m\geq2$. How do I calculate the topological entropy of the map $E_{m}\colon[0,1)\to[0,1)$ defined by $$E_{m}(x)=\begin{cases}mx&0\leq x<1/m\\ mx-1&1/m\leq x<2/m\\ \vdots&\vdots\\ mx-(m-1)&(m-1)/m\leq x<1\end{cases},$$ using spanning/separating sets or covering families?
2026-03-27 00:06:47.1774570007
Topological entropy of $[0,1)\to[0,1), \ x\mapsto mx$ modulo $1$
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