Dynamical Systems

Wolf, et al., "Determining Lyapunov Exponents from a Time Series"

Extensively referenced.

https://drive.google.com/open?id=0B9oPg7GYw1qnSC1Ma05LRHlfTVU

Sandri, M., "Numerical Calculation of Lyapunov Exponents"

Good overview of dynamical systems with numerical calculations of Lyapunov exponents.

https://drive.google.com/open?id=0B9oPg7GYw1qnTnIwenl0Y0lrbTg

Lagrangian Coherent Structures and chaotic mixing - 15 minute tutorial

https://drive.google.com/open?id=0B9oPg7GYw1qnYl82UDhCVFkwVlE

Robins et al., "Topology and Intelligent Data Analysis" (2004)

https://drive.google.com/open?id=0B9oPg7GYw1qnZGRfU2doMVJVMFU

Fractal dimensions from pixels of 2-D video display of complex system

Just wanted to capture this -- not sure if I completely understand it.

It is possible to determine the fractal dimension of a 2-D projection of a complex system by counting the number of pixels (i.e., boxes of side epsilon) for ever-decreasing values of epsilon, and plotting the results on a log-log plot. The result should be a straight line and the slope is the fractal dimension of the system.