The object of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems. Such important mechanical systems exhibit interesting dynamic behaviors: homoclinic orbits; sub-harmonic responses; amplitude modulations and chaos. These dynamics have been obtained numerically and in some case have been experimentally observed. Using recent techniques of the Nonlinear Time Series analysis, the response of axially moving systems is studied for a large variety of test cases. The correlation dimension of the time series, which is deeply related to the minimal dimension of a system able to reproduce the dynamics, is estimated. Lyapunov exponents are evaluated in order to quantify the response regularity. The present work give a contribution in understanding complex dynamics observed both in conservative and dissipative systems. The dynamical phenomena are analyzed within the unified framework fo the Nonlinear Time Series Analysis. In the case of experimental data the new nonlinear filtering techniques, based on the embedding techniques, have been applied to reduce high noise when classical techniques give bad results.

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