Pinching deformations of rational maps
by O'Connell, Robert, Ph.D., INDIANA UNIVERSITY, 2009, 67 pages; 3354918

Abstract:

Let f be a rational map defined on the Riemann sphere. Then f defines a dynamical system whose chaotic locus is called the Julia set. A pinching deformation, ft, t > 0, is a one-parameter family of deformations of f. It is a way to create a parabolic cycle by forcing an attracting cycle and a repelling cycle to collide. The main result shows that for certain pinching deformations, if ft → g uniformly, then the Julia set of ft converges in the Hausdorff topology to the Julia set of g in the Hausdorff topology.
 
AdviserKevin M. Pilgrim
SchoolINDIANA UNIVERSITY
SourceDAI/B 70-04, p. , Jul 2009
Source TypeDissertation
SubjectsMathematics
Publication Number3354918
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