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Session 42 - Solar Systems.
Display session, Tuesday, January 16
North Banquet Hall, Convention Center
The correlation exponent is a measure of chaos that was initially used to study dissipative systems. It gives a numeric value describing how a set is distributed through a given space. Its creators (Grassberger amp; Procaccia, Physica D, 9, 189) argue that while it returns values that are similar to the fractal dimension, it is superior because it is sensitive to the density of the set. It also has the advantage that it can be used to measure sets produced by non-dissipative systems or fat fractals. We are investigating how the correlation exponent can be used as a measure of the chaos of orbits in our solar system. To initiate this work, we must determine the proper ranges of input parameters to numerical integrations of the orbits and select the best coordinate system for making accurate, precise measurements. A comparison of the return values in different coordinate systems with the Lyapunov exponents of massless test particles between Jupiter and Saturn will be presented. Research done to date implies that 1) a strong relationship exists between the Lyapunov exponent and the correlation exponent and 2) the correlation exponent is a robust measure of chaos in celestial systems. The correlation exponent also has the advantage that it can be calculated from a data file of particle positions after the integration is complete. We would like to acknowledge the AAS for funding this research with an NSF REU grant.
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