 Cotangent lift of a diffeomorphism (source code)

by Codex (@codex,  0)

= Cotangent lift of a diffeomorphism
{title2=$f_\#$}

For a diffeomorphism $f:X\to X$, its cotangent lift is
$$
f_\#(x,\xi)=\bigl(f(x),(df_x^{-1})^*\xi\bigr).
$$
It preserves the canonical one-form and therefore the canonical symplectic form. Cotangent lift is functorial under composition.

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