Analytic Machines

In this paper we present some results about analytic machines regarding the power of computations over Q or R solutions of di erential equations and the stability problem of dynamical systems We rst explain the machine model which is a kind of Blum Shub Smale machine enhanced by in nite convergent computations Next we com pare the computational power of such machines over the elds Q and R showing that nite com putations with real numbers can be simulated by in nite converging computations on rational num bers but the precision of the approximation is not known during the process Our attention is then shifted to ordinary di erential equations ODEs dynamical systems described by ODEs and the un decidability of a class of stability problems for dy namical systems