= Hofer metric
{c}
{title2=$d_H(\phi,\psi)=\inf_{\phi_H^1=\phi^{-1}\psi}\int_0^1(\max H_t-\min H_t)\,dt$}
= Hofer's metric
{c}
{synonym}
The displayed distance uses the oscillation length of a compactly supported <Hamiltonian isotopy>. On a closed manifold one may normalize each Hamiltonian to have zero mean. Additive time-dependent constants do not change the flow or its oscillation. Pullback by a <symplectomorphism> preserves extrema, so this distance is bi-invariant. Nondegeneracy requires an additional geometric argument; it does not follow merely from the definition as an infimum of path lengths.
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