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Conjugacy and Symbolic Dynamics: The Logistic Map, An Example

Student-Run Applied & Math Seminar

Speaker: Nick Travers, UC Davis
Location: 2112 MSB
Start time: Wed, Apr 29 2009, 12:10PM

Two maps f:X->X and g:Y->Y are conjugate if there exists a homeomorphism h:X->Y s.t. f = h-1 of g of h. Maps which are conjugate have essentially the same dynamics, and so often one may attempt to analyze the behavior of a given (hard to analyze) map f by finding a conjugacy to a simpler map g. In particular, one may look for conjugacies (or semi-conjugacies) into shift spaces over finite alphabets of symbols, and study the 'symbolic dynamics' on these shift spaces. If such conjugacies can be found the dynamics will generally become quite transparent. We will present an informal introduction to these methods using the logistic map as an example.