Julia Sets and Symbolic Dynamics of Certain Rational and Entire Functions

77 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.A complex analytic map f always decomposes the complex plane into two dis-joint subsets, the Julia set J(f) on which the family of iterates of f, $\{f\sp{k}\}\sbsp{k=0}{\infty}$, fails to be a normal family, and its complement, the Fatou set F(f). The dynamics of f on its Fatou set is relatively tame while the dynamics on its Julia set is always complicated. We study the Julia sets and Symbolic dynamics of certain rational and entire functions. We also estimate the size of some Julia sets in terms of their Hausdorff dimension.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD