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[scalar_dynam] Add an example to local stability #521

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longye-tian opened this issue Jul 22, 2024 · 1 comment
Closed

[scalar_dynam] Add an example to local stability #521

longye-tian opened this issue Jul 22, 2024 · 1 comment

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@longye-tian
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longye-tian commented Jul 22, 2024

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

@longye-tian
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This issue is now closed by #523.

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