Total convergence or general divergence in Small Divisors

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the potential theory sense. We illustrate this general principle in different problems of small divisors

Ergodic solenoids and generalized currents

We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids with a transversal measure into smooth manifolds, generalizing Ruelle-Sullivan currents.Comment: 28 pages, 2 figures. Fully revised presentation of the paper. Accepted in Revista Matematica Complutense. The final publication is available at http://www.springerlink.co