Show simple item record

dc.contributor.authorDoyle, John Robert
dc.date.accessioned2014-08-20T04:30:11Z
dc.date.available2014-08-20T04:30:11Z
dc.date.issued2014-05
dc.identifier.otherdoyle_john_r_201405_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/doyle_john_r_201405_phd
dc.identifier.urihttp://hdl.handle.net/10724/30397
dc.description.abstractIn 1998, Poonen gave a conjecturally complete classification of the possible preperiodic structures for quadratic polynomials defined over Q. In this thesis, we prove a number of results toward a similar classification, but over quadratic extensions of Q. In order to do so, we formalize a more general notion of emph{dynamical modular curve} in the setting of quadratic polynomial dynamics. We also discuss the geometry of these curves, proving in some cases that they are irreducible over C, extending a result of Bousch.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectArithmetic dynamics
dc.subjectpreperiodic points
dc.subjectuniform boundedness conjecture
dc.subjectquadratic polynomials
dc.subjectdynamical modular curves
dc.subjectquadratic fields
dc.titleDynamics of quadratic polynomials over quadratic fields
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorRobert Rumely
dc.description.committeeRobert Rumely
dc.description.committeeRobert Varley
dc.description.committeeDino Lorenzini
dc.description.committeePeter Clark


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record