Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.4, pp.362--375

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 4, pp.362--375

An Example of Interplay Between Theoretical Results on the Structure of Dynamical Systems and Numerical Experiments Based on Mapping Modeling.
Claude Froeschlé and Elena Lega

Starting from a recent mathematical result concerning the structure around invariant KAM tori we show how numerical experiments using mapping as model problem allow to "visualize" and extend to a physical domain results which could remain only of mathematical interest and somehow far from the real application to dynamical systems. The feasibility of the numerical experiments mainly depends on the sensitivity and on the computational cost of tools of detection of weak chaos. We present the most important tools and deeply compare each other in the aim of giving a global description of the actual state of numerical methods of analysis.
Key words: chaos, dynamical systems, mapping modeling, numerical experiment

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