Let $Z(u,v)$ be the vector field $Z(u,v)=(u^2+u,v^2+v)$, let $\Gamma_t$ denote its flow. I have shown that $[X,Z]=Z-X$.
Show that $(\Gamma_t)_*X=e^{-t}X-(e^{-t}-1)Z$.
Could someone please show me how to do this please.
2026-03-30 09:49:47.1774864187
Identity of the pushforward of a vector field using a Jacobi bracket.
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