Characterization of Chaos: A New, Fast, and Effective Measure

• Published in: Annals of the New York Academy of Sciences Vol. 1045; no. 1; pp. 79 - 92
• Main Author: SIDERIS, IOANNIS V.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.2005
• Subjects: Chaos theory; chaotic dynamics; chaotic measures; Degrees of freedom; Dynamical systems; Dynamics; Evolution; Mathematical analysis; nonlinear dynamics; Orbitals; Orbits; stickiness; transient chaos
• ISSN: 0077-8923; 1749-6632
• DOI: 10.1196/annals.1350.008

: A new technique for characterization of the regular or chaotic nature of dynamical orbits has been discovered. It takes advantage of morphological and dynamical properties of orbits, and is very effective, at least for tim‐independent systems with two degrees of freedom. The new technique was initially designed with time‐dependent and N‐body systems in mind. For this reason one of its main goals is to provide straightforward information about the transient chaos associated with such regimes. Equally important is the distinction it can provide between sticky and wildly chaotic epochs during the evolution of chaotic orbits. The most important advantage over the existing methods is that it can characterize an orbit using a very small number of orbital periods. For these reasons the new method is extremely promising to be useful and effective in a broad spectrum of disciplines.