Index of a planar periodic orbit
= Index of a planar periodic orbit
A planar <periodic orbit>, oriented by the flow, has <Poincaré index> $+1$. The index theorem equates this with the sum of the indices of the isolated equilibria enclosed by the orbit. A hyperbolic equilibrium has index $+1$ when its <Jacobian matrix> has positive determinant and index $-1$ when it is a <saddle equilibrium>.