The number of these objects can be computed by taking the alternating trace of the Frobenius endomorphism, as shownby the Lefschetz trace formula. For an unperturbed rational curve with a speciÂfied rotation number, only an 
The number of these objects can be computed by taking the alternating trace of the Frobenius endomorphism, as shownby the Lefschetz trace formula. For an unperturbed rational curve with a speciÂfied rotation number, only an even numberof these objects will remain aftfter a perturbation, and they will be alternately elliptic and hyperbolic, as per a theorem namedafter Poincare and Birkhho. One of these is stable if both eigenvalues of its stability matrix are negative, or alternately ifits Lyapunov exponent is negative. For the logistic map, these exist at 0 and 1 minus quantity 1 over mu. For a continuousreal-valued function on some closed interval, an application of the intermediate value theorem can be used to show that oneof these values must exist on that interval; that theorem is a special case of a theorem which guarantees the existence of oneof these values for any continuous mapping from the n-dimensional unit ball to itself, named for Brouwer. For 10 points,identify these values which equal the application of some map to themselves.
The number of these objects can be computed by taking the alternating trace of the Frobenius endomorphism, as shownby the Lefschetz trace formula.
fixed point or equilibrium point or invariant point