The parameter space of a family of quadratic polynomial maps of <math> <?Pub Eqn> <f> <blkbd>C^<rm>2</rm></blkbd></f> </math>.

In one dimensional complex dynamics, the study of the parameter space of the quadratic family fc(z) = z2 + c has led to discovery of the celebrated Mandelbrot set. However, in higher dimensions, the parameter space is not well understood and no appropriate analog of the Mandelbrot set is known. This thesis describes the parameter space of a two-dimensional quadratic family of polynomial maps of C2 and investigates what would represent an appropriate analog of the Mandelbrot set in the two dimensional setting. Two subsets of the parameter space, which share several common features with the one-dimensional Mandelbrot set, are considered for study. Some of their properties are investigated by using the sum of the Lyapunov exponents.PhDMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125609/2/3208417.pd