Continued Fractions and Other Mathematical Adventures
November 11, 2014
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 at 4:45pm
Continued fractions are dated back to as early as Euclid's elements, but they were first phrased by John Wallis. Euler, Lagrange, and Galois are among mathematicians who studied continued fractions. In this talk, we view continued fractions from the perspective of semigroup actions. Lagrange, for example, showed that quadratic irrationals have periodic continued fractions. Our main objective is to discuss a related density result that describes pairs of linear fractional transformations whose generated semigroup has dense fixed point sets. Along the way, we discuss topics such as rational approximations, golden ratio and Fibonacci numbers, linear fractional transformations, discrete dynamical systems, and chaos.
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