We study polynomials with coefficients in a field L as dynamical systems where L is any algebraically closed and complete ultrametric field with dense valuation group and characteristic zero residual field. We give a complete description of the dynamical and parameter space of cubic polynomials. In particular we characterize cubic polynomials with compact Julia sets. Also, we prove that any inf...

For all hyperbolic polynomials we proved in [11] a Lipschitz estimate of Jacobi matrices built by orthogonalizing polynomials with respect to measures in the orbit of classical Perron-Frobenius-Ruelle operators associated to hyperbolic polynomial dynamics (with real Julia set). Here we prove that for all sufficiently hyperbolic polynomials this estimate becomes exponentially better when the dim...

This paper presents a switch methodology together with a sum of squares (SOS) techniques to synthesize a nonlinear controller for a polynomial Takagi-Sugeno (TS) fuzzy model. A polynomial T-S fuzzy model adopts a polynomial representation of the nonlinear dynamics in its consequent part, which make it less susceptible to linearization errors. With respect to polynomial T-S fuzzy models, a fuzzy...

In this paper are characterized the polynomials, in terms of their coefficients, that have all their orbits dense in the set of 3-adic integers Z3.

Loudspeakers always introduce linear and nonlinear distortions in a stereo system. It is however possible to partially cancel these distortions by digitally pre-inverting the signal. We here discuss one of several possible solutions to this problem, namely the use of a linear inverse obtained from a measured ARX loudspeaker model. The inverse is obtained by well known polynomial methods as a H2...

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron...

A new approach for modelling the dynamics of gene expression from time series microarray data is presented. A modelling method based on a continuous representation of Boolean functions in the form of Zhegalkin Polynomials is proposed. Structural information known from theoretical biology like the canalizing property can be included as well as continuous measurements of gene expression levels. A...