Spectra of linear fractional composition operators on H-2(B-N)

We characterize the spectra of composition operators on the Hardy space H-2(B-N), when their symbols are elliptic or hyperbolic linear fractional self-maps of the unit ball B-N. Therefore, combining with the result obtained by Bayart, the spectra of all linear fractional composition operators on H-2(B-N) are completely determined.