Lower dimensional invariant tori for quasiperiodically forced circle diffeomorphisms

For any analytic quasiperiodically forced circle diffeomorphisms (omega, < p/q, omega > + epsilon f), where f is fixed and epsilon is small, we show that if w is Diophantine and the fibred rotation number of the diffeomorphism remains constant in a unilateral neighborhood of epsilon = 0 (i.e., there is a unilateral phase-locking at epsilon = 0), then the diffeomorphism has at least one analytic q-invariant torus, provided epsilon is small enough. (C) 2012 Elsevier Inc. All rights reserved.