Determination of the Total Number of Isolating Integrals Using the Correlation Integral

Details Determination of the Total Number of Isolating Integrals Using the Correlation Integral Determination of the Total Number of Isolating Integrals Using the Correlation Integral

May 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009rmxac..35..295c&link_type=abstract

XII Latin American IAU Regional Meeting (Eds. G. Magris, G. Bruzual, & L. Carigi) Revista Mexicana de Astronomía y Astrofísica (

Other

Scientific paper

There are several available numerical tools that can be used to ascertain how many isolating integrals of the movement has a stellar orbit. The Lyapunov exponents, for example, allow to determine whether a 3D orbit has zero, one, two or more than two isolating integrals (zero, one or more than one for 2D orbits). That is, it cannot be specified how many isolating integrals are satisfied by a regular orbit. This is a common feature shared by any chaos-finder numerical algorithm. On the other hand, there are techniques that allow to determine how many isolating integrals a regular orbit has (v.g., spectral stellar dynamics, frequency maps, etc.), but that are useless in order to specify the number of isolating integrals possessed by a chaotic orbit. The correlation integral is an easy-to-use tool that allows to compute the dimension of the phase space which an orbit in an arbitrary dynamical system is moving in. In a stellar dynamical context, this can be used to compute how many isolating integrals has the orbit, irrespective of it being regular or chaotic. However, its implementation should be done with care, due to numerical subtleties that may conceal the true result.

Affiliated with

Also associated with

No associations

Rating

Determination of the Total Number of Isolating Integrals Using the Correlation Integral does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Determination of the Total Number of Isolating Integrals Using the Correlation Integral, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determination of the Total Number of Isolating Integrals Using the Correlation Integral will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1111491