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Homework Statement
Show that the following vector field on the cylinder has a periodic orbit,
v' = -v
Θ' = 1
Homework Equations
Bendixson's theorem: Suppose D is a simply connected open subset of R^2. If the expression div(f,g) = ∂f/∂x + ∂g/∂y is not identically zero and does not change the sign in D, the there are no periodic orbits in the autonomous system in D.
The Attempt at a Solution
f = v' =-v
g = Θ' = 1
div(f,g) = -1 which would mean there are no periodic orbits or am I missing something??
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