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MCU

2007

2007

We review some results about the computational power of several computational models. Considered models have in common to be related to continuous dynamical systems. 1 Dynamical Systems and Polynomial Cauchy Problems A polynomial Cauchy problem is a Cauchy problem of type x = p(x, t) x(0) = x0 where p(x, t) is a vector of polynomials, and x0 is some initial condition. The class of functions that are solution of a polynomial Cauchy problem turns out to be a very robust class [14]. It contains almost all natural mathematical functions. It is closed under addition, subtraction, multiplication, division, composition, diﬀerentiation, and compositional inverse [14]. Actually, every continuous time dynamical system x = f(x, t) where each component of f is deﬁned as a composition of functions in the class and polynomials can be shown equivalent to a (possibly higher dimensional) polynomial Cauchy problem [14]. This implies that almost all continuous time dynamical systems considered in boo...

Related Content

Added |
30 Oct 2010 |

Updated |
30 Oct 2010 |

Type |
Conference |

Year |
2007 |

Where |
MCU |

Authors |
Olivier Bournez, Emmanuel Hainry |

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