Gonzalez Tokman, CeciliaThis thesis is concerned with the study of quantitative aspects of the stability of some dynamical systems that exhibit hyperbolic features. Results include scaling laws for bubbling bifurcations, description of limit invariant measures for metastable systems and shadowing properties of a data assimilation algorithm in the context of hyperbolic systems.DissertationMathematicsBifurcationsData AssimilationEnsemble Kalman FilterHyperbolic DynamicsPiecewise Smooth Metastable SystemsScaling Laws