Seminar on Industrial Problems

Symbolic Dynamics in Mathematics, Physics, and Engineering

September 26, 1997

Presented by: Nick Tufillaro, Hewlett-Packard

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Applications of symbolic dynamics from mathematics, physics, and engineering are discussed. Results from braid theory allow one to generalize ideas about unimodal interval maps to two-dimensional ``single-fold" maps. These results from topological dynamics are then used to help unravel the dynamical motions of experiments with a mechanical string. Finally, a more empirical approach to the symbolic analysis of time series is used to resolve a long standing problem of cycle-variability in internal combustion engines. In each of these examples a symbolic analysis is utilized to help identify nonlinear models and parameters.

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