Conical limit sets of hyperbolic subgroups

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Given a hyperbolic subgroup H of a hyperbolic group G for which a Cannon-Thurston map i:∂ H ∂ G exists, we study the limit set Λₕ of H with respect to its action on ∂ G. We prove that the set of conical limit points is exactly the subset of Λₕ consisting of the points to which the Cannon-Thurston map i injects. Moreover, we show that when H is not quasi-convex in G, there exists a non-conical limit point in Λₕ