The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the… Expand

In this paper, we show that there are initial value problems defined with polynomial ordinary differential equations that can simulate universal Turing machines in the presence of bounded noise.Expand

We show that, in an appropriate framework, the GPAC and computable analysis are actually equivalent from the computability point of view, at least in compact intervals.Expand

We show that the solution of a locally Lip- schitz differential equation is computable even if the function is not effectively locally Lipschitz, and recover a result of Ruohonen, in which it is shown that if the solution is unique, then it is.Expand

We show that the solution of a differential equation defined by a locally Lipschitz function is computable even if the right-hand side is not effectively locally Lippingchitz.Expand

We consider the General Purpose Analog Computer (GPAC), introduced by Claude Shannon in 1941 as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later electronic) machines of that time.Expand

Nonlinear dynamical systems abound as models of natural phenomena. They are often characterized by highly unpredictable behaviour which is hard to analyze as it occurs, for example, in chaotic… Expand

As one of the seven open problems in the addendum to their 1989 book Computability in Analysis and Physics Pour-El and Richards (1989) [17], Pour-El and Richards asked, ''What is the connection… Expand