Quasiconformal mappings in the complex plane

dc.contributor.advisorStankewitz, Richard L.en_US
dc.contributor.authorMercer, Nathan T.en_US
dc.date.accessioned2011-06-03T19:41:03Z
dc.date.available2011-06-03T19:41:03Z
dc.date.created2006en_US
dc.date.issued2006
dc.description.abstractIt is well known that, as a consequence of the Identity Theorem, we cannot "glue" together two analytic functions to create a new globally analytic function. In this paper we will both introduce and investigate special homeomorphisms, called quasiconformal maps, that are generalizations of the well known conformal maps. We will show that quasiconformal maps make this "gluing," up to conjugation, possible. Quasiconformal maps are a valuable tool in the field of complex dynamics. We will see how quasiconformal maps of infinitesimal circles have an image of an infinitesimal ellipse. Although quasiconformal maps are nice homeomorphisms, they might only be differentiable in the real sense almost everywhere and, surprisingly, complex differentiable nowhere. We shall rely on the work of Lehto and Virtanen as well as Shishikura in exploring these interesting complex valued functions.
dc.description.degreeThesis (M.S.)
dc.description.sponsorshipDepartment of Mathematical Sciences
dc.format.extent77 leaves : ill. ; 28 cm.en_US
dc.identifierLD2489.Z78 2006 .M47en_US
dc.identifier.cardcat-urlhttp://liblink.bsu.edu/catkey/1348866en_US
dc.identifier.urihttp://cardinalscholar.bsu.edu/handle/20.500.14291/188151
dc.sourceVirtual Pressen_US
dc.subject.lcshQuasiconformal mappings.en_US
dc.subject.lcshFunctions of complex variables.en_US
dc.titleQuasiconformal mappings in the complex planeen_US
Files
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.98 KB
Format:
Item-specific license agreed upon to submission
Description:
Collections