We give a constuction of the JSJ splitting of a one-ended hyperbolic group, using the separation properties of local cut points in the boundary. We deduce that the JSJ splitting in this case is quasiisometry invariant. We also see that a one-ended non-fuchsian hyperbolic group splits over a two-ended subgroup if and only if it has a local cut point in the boundary. As a corollary, we obtain an annulus theorem for hyperbolic groups. The proofs involve analysing the dynamics of convergence actions on Peano continua.
Acta Math. 180 (1998) 145-186.