arXiv subjects

D. Pingel

Publications and source records attributed to D. Pingel.

3 recordsLinked to original sources

arXiv1999

A Stochastic Approach to the Construction of One-Dimensional Chaotic Maps with Prescribed Statistical Properties

We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power of our method.

chao-dyn↗

arXiv1998

General theory and examples of the inverse Frobenius-Perron problem

The general solution of the inverse Frobenius-Perron problem considering the construction of a fully chaotic dynamical system with given invariant density is obtained within the class of one-dimensional unimodal maps. Some interesting connections between this solution and the approach via conjugation transformations are eluminated. The developed method is applied to obtain a wide class of maps having as invariant density the two-parametric beta-probability density function. Varying the parameters of the density a rich variety of dynamics is observed. Observables like autocorrelation functions, power spectra and Lyapunov exponents are calculated for representatives of this family of maps and some theoretical predictions concerning the decay of correlations are tested.

chao-dyn↗

arXiv1997

Analytical solutions to one-dimensional dissipative and discrete chaotic dynamics

Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time correlation function. We illustrate our solutions by means of a few examples for which conventional numerical trajectory calculations fail to predict the correct behaviour.

chao-dyn↗