Diffeomorphism

Flow on a manifold

Let be a -manifold with group of diffeomorphisms . A (local) 1-parameter group is called a (local) flow on . #m/def/geo/diff The orbit of a point defines a -curve

with . The map

defines a -vector field , called the infinitesimal generator of .

Conversely, given a vector field , one can (usually) find a corresponding local flow whose orbits are called integral curves.

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