TITLE: Manifolds at the verge of a hyperbolicity breakdown AUTHORS: Alex Haro (1) and Rafael de la Llave (2) (1) Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona (Spain) E-mail: haro@mat.ub.es (2) Department of Mathematics, University of Texas at Austin, Austin, TX 78712 (USA). E-mails: llave@math.utexas.edu ABSTRACT: We study numerically the disappearance of invariant objects in quasi-periodic systems and identify a scenario for breakdown. In this scenario, the disappearance happens because the stable directions of the normal dynamics become close to the unstable directions. We identify remarkable quantitative regularities, namely that the distance between the stable and unstable directions and the Lyapunov multipliers have power law dependence with the parameters. The exponents of the power laws are universal.