Lower bounds on entropy via the Conley index with application to time series

AbstractA proof of a localized version of the proven entropy conjecture for C∞ smooth maps is given. This allows for computational methods for bounding topological entropy through properties of the Conley index. Chaos can then be determined by a non-global index calculation robust under possibly large (and noisy) perturbations. In addition, a proof of a Wazewski's Principle for time series analysis is given which allows for lifting of entropy to the observed dynamical system under certain conditions