title: Statistically relaxing to generating partitions for observed time-series data.
abstract: We introduce a relaxation algorithm to estimate approximations to generating partitions for observed dynamical time series. Generating partitions preserve dynamical information of a deterministic map in the symbolic representation. Our method optimizes an essential property of a generating partition: avoiding topological degeneracies. We construct an energy-like functional and use a nonequilibrium stochastic minimization algorithm to search through configuration space for the best assignment of symbols to observed data. As each observed point may be assigned a symbol, the partitions are not constrained to an arbitrary parametrization. We further show how to select particular generating partition solutions which also code low-order unstable periodic orbits in a given way, hence being able to enumerate through a number of potential generating partition solutions.
authors.affiliation: Institute For Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA. mbuhl@clack.ucsd.edu
authors.forename: Michael
authors.initials: M
authors.lastname: Buhl
authors.forename: Matthew B
authors.initials: MB
authors.lastname: Kennel