The fixed group of an automorphism of a word hyperbolic group is rational

[C1] Cooper, D.: Automorphisms of free groups have finitely generated fixed point set. (Preprint, Princeton, 1983) [C2] Cooper, D.: Automorphisms of negatively curved groups. (Preprint. Santa Barbara, March 1989) [ECLHPT] Epstein, D.B.A., Cannon, J.W., Holt, D.F., Levy, S.V.F., Paterson, M.S., Thurston, W.P.: Word Processing in Groups. Boston: Jones and Bartlett 1992 [G] Gersten, S.M.: Fixed points of automorphisms of free groups. Adv. Math.64, 51–85 (1987) [GS] Gersten, S.M., Short, H.B.: Rational subgroups of biautomatic groups. Ann. Math.134, 125–158 (1991). [GT] Goldstein, R.Z., Turner, E.C.: Automorphisms of free groups and their fixed points, Invent. Math.78, 1–12 (1984). [NS] Neumann, W.D., Shapiro, M.: Equivalent automatic structures and their boundaries. Int. J. Alg. Comp. (to appear) [P] Paulin, F.: Points fixes d'automorphismes de groupes hyperboliques. Ann. Inst. Fourier39, 651–662 (1989). [S] Stallings, J.R.: Graphical theory of automorphisms of free groups. In: Gersten, S.M., Stallings, J.R. (eds.) Combinatorial Group Theory and Topology. (Ann. Math. Stud., vol. 111, pp. 79–105): Princeton, Princeton University Press 1987