dI proves a formula P
to be a differential invariant, i.e., true locally in the direction of the dynamics by reducing it to its differential (P)'
after assigning the right-hand side f(x)
of the ODE to its left-hand side x'
.
Rule dI reduces a property of an ODE x'=f(x)
to a property of a discrete assignment x':=f(x)
.
The resulting formula [x':=f(x)](P)'
is the Lie-derivative of P
along the ODE x'=f(x)
.
See also
Learning resources