Symbolic Dynamics in Mathematics, Physics, and Engineering
نویسنده
چکیده
We discuss several applications of symbolic dynamics and topological analysis to problems in mathematics, physics, and engineering, based on a talk presented by Dr. 1. Introduction In September of 1997, Nick Tuullaro discussed some applications of symbolic dynamics to problems in mathematics, physics, and engineering in an IMA Industrial Problems Seminar. This article will discuss some of the applications from Nick's talk. The mathematical aspects of Nick's discussion included several topics, including kneading theory, horseshoes, and braid analysis. Two systems that he discussed were the quadratic map (and other unimodal maps), and the Rossler system of diierential equations. Some problems from physics that Nick discussed were the vibrating string and the Belousov-Zhabotinskii reaction. The goals of an engineering application might include a problem such as detecting bifurcations in noisy experimental data. As an example from engineering, Nick discussed an application of symbolic dynamics in the study of cycle variability in internal combustion engines. The diierent emphasis of the applications in the diierent disciplines is summarized in Table 1. The recent applications in physics and engineering suggest that symbolic dynamics is emerging as a powerful tool in nonlinear system identiication. Nick outlined the general strategy for using symbolic dynamics as an analysis tool as follows:
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Symbolic Dynamics in Mathematics, Physics, and Engineering
I discuss several applications of symbolic dynamics and topological analysis to problems in mathematics, physics, and engineering. These are notes based on a talk presented on September 26, 1997 at the Institute for Mathematics and its Applications (IMA http://www.ima.umn.edu) as part of their Industrial Problems Seminar. The IMA is located in the Mathematics Department at the University of Min...
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