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Unformatted text preview: . • Thus d dt ( f ◦ ϕ t ) ² ² ² ² t = = X ( f ) . • Let Y be another vector ﬁeld on M . • Then d dt Y (( f ◦ ϕ t )) ² ² ² ² t = = Y ( X ( f )) . • Then at the point ϕ t ( x ) we have two di ﬀ erent well deﬁned vectors, Y ϕ t ( x ) and ϕ t * Y x . • Diagram. • Deﬁnition 5.1.1 A vector ﬁeld Y is invariant under the ﬂow ϕ t generated by a vector ﬁeld X if Y ϕ t ( x ) = ϕ t * Y x . An invariant vector ﬁeld Y is also called a Jacobi ﬁeld . di ﬀ geom.tex; April 12, 2006; 17:59; p. 108...
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 Spring '10
 Wong
 Geometry, Derivative, Continuous function, Vector field, Smooth function

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