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orbdim - compute dimensionaly of phase space for an orbit


orbdim in=orbit [parameter=value]


orbdim computes the dimensionalty of phase space for an orbit. It uses the method described by Carnevalli and Santangelo.

Other methods, such as SALI (see Manos & Athanassoula), exist.

orbdim needs a lot of data before the exponent can be reliably determined. In practice a 3 dimensional orbit is excluded from this analysis. It can be done with 2 dimensional orbits though.


The following parameters are recognized in any order if the keyword is also given:
input file, in orbit(5NEMO) format [no default]


A number of Chaos Indicators (CI) are listed by Carpinetro et al:
LIs: Lyapunov Indicators (there are several)
MEGNO: Mean Exponential Growth factor of Nearby Orbits 
SElLCE: Slope Estimation of the largest Lyapunov Characteristic Exponent

SALI: Smaller ALignment Index 
GALI: Generalized ALignment Index 
FLI: Fast Lyapunov Indicator 
OFLI: Orthogonal Fast Lyapunov Indicator 
SD: Spectral Distance
SSNs: dynamical Spectra of Stretching Numbers 
RLI: Relative Lyapunov Indicator

See Also

Carnevali, P. and Santangelo, P., 1984. ApJ 281 473-476.
Manos, T and Athanassoula, E. - Smaller Alignment Index (SALI)
Carpintero, D.D. -     arXiv:0805.2532v1 (2008)
Maffione et al. - arXiv:1108.5481v1 (2011) - MEGNO (Mean Exponential Growth
factor of Nearby Orbits)
Zotos - arXiv:1209.1708 - the f-indictor as an indicator for chaos detection
Carpintero et al 2014 - LP-VIcode - - 


Peter Teuben


pollux:/usr3/teuben/orbit    authors original sources

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