Analytic machines

In this paper we present some results about analytic machines regarding the power of computations over Q or R, solutions of differential equations and the stability problem of dynamical systems. We first explain the machine model, which is a kind of Blum-Shub-Smale machine enhanced by infinite convergent computations. Next, we compare the computational power of such machines over the fields Q and R showing that finite computations with real numbers can be simulated by infinite converging computations on rational numbers, but the precision of the approximation is not known during the process. Our attention is then shifted to ordinary differential equations (ODEs), dynamical systems described by ODEs and the undecidability of a class of stability problems for dynamical systems