Unformatted text preview: ) ∈ G . Note that the last condition is equivalent to (iv): f ( x,y ) ∂V ∂x + g ( x,y ) ∂V ∂y ≤ Poincare-Bendixson Theorem Suppose that for some initial condition the solution ( x ( t ) ,y ( t )) enters and does not leave some closed, bounded domain D , and that there are no stationary points in D . Then there is at least one periodic orbit in D ....
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- Fall '08
- Critical Point, Open set, Stationary point, Dynamical systems, Lyapunov, Lyapunov function