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Dear John @jstac ,
According to #426, we need an example for local stability that is not globally stable.
I propose to use example in DP book 1, as follows
Consider the self-map $g$ on $\mathbb{R}$ defined by $g(x)=x^2$. The fixed point $1$ is not stable.
For example, $g^t(x)\to\infty$ for any $x>1$.
However, $0$ is locally stable, because $-1<x<1$ implies that $g^t(x)\to 0$ as $t\to \infty$.
Best ❤️
Lonyge
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