Suppose I have a map $T:[-1,1]\to [-1,1]$. If I want to view this as a map from $[0,1]\to [0,1]$, I change my cooridnates such that $\bar{x}=(x+1)/2$ and let $\bar{T}(\bar{x})=(T(\bar{x})+1)/2$. Will the maps $T$ and $\bar{T}$ have the same properties? Certainly they will have the same number of fixed points but they will just be translated. Is studying $\bar{T}$ equivalent to studying the map $T$? Is there possibly a reference which describes the relationship between these maps?
2026-04-13 19:24:05.1776108245
Rescaling axis changes properties of map
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