Second-Order Chaos Indicators MEGNO2 and OMEGNO2: Theory

Modifications of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) linear variational method called MEGNO2 and OMEGNO2 indicators are introduced. The modifications are based on taking into account not only the linear, but also the nonlinear part of the increment of the phase flow in the di...

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Veröffentlicht in:	Russian physics journal 2018-02, Vol.60 (10), p.1728-1738
1. Verfasser:	Shefer, V. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	CHAOS THEORY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Condensed Matter Physics Divergence DYNAMICAL SYSTEMS Hadrons Heavy Ions Indicators Lasers Liapunov exponents LYAPUNOV METHOD Mathematical and Computational Physics NONLINEAR PROBLEMS Nuclear Physics Optical Devices Optics ORBITS PERIODICITY Photonics Physics Physics and Astronomy Theoretical TRAJECTORIES VARIATIONAL METHODS
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Zusammenfassung:	Modifications of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) linear variational method called MEGNO2 and OMEGNO2 indicators are introduced. The modifications are based on taking into account not only the linear, but also the nonlinear part of the increment of the phase flow in the divergence among nearby trajectories according to the second-order formulas. The new indicators allow one to determine more quickly the nature of the orbits under study in dynamical systems with zero or small Lyapunov exponents in comparison with the first-order variational indicators. They improve the analysis of regular regions and, in particular, periodic orbits as well as prevent the appearance of spurious structures in the resulting mappings.
ISSN:	1064-8887 1573-9228
DOI:	10.1007/s11182-018-1275-z