Reconstructing phase space and estimating maximal Lyapunov exponent from experimental time series

Written by Ian Kilgore in math on Sun 26 July 2015. Tags: chaos, geometry, research, experimental data,

In the course of my research I needed to demonstrate that some experimental data is chaotic. This post is an example of how I reconstruct phase space from 1-D experimental data by the method of delays, plot the underlying attractor, and estimate the maximal Lyapunov exponent (characterizing the divergence of the system).

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Inverse-Square Laws: A Physical Consequence of the Geometry of Space

Written by Ian Kilgore in math on Wed 10 September 2014. Tags: physics, geometry, kant, math,

The ubiquitous inverse-square laws in physics are a necessary consequence of the three-dimensional nature of space. Barrow shows that Kant was the first to recognize the geometrical connection, although he got it backwards. I explain the geometrical reason for inverse-square laws and follow Kant's argument. Thanks, Kant. Thant.

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