# Polydegree properties of polynomial automorphisms

 dc.contributor Dixon, Martyn R. dc.contributor Evans, Martin J. dc.contributor Corson, Jon M. dc.contributor Borie, Richard B. dc.contributor.advisor Lewis, Drew dc.contributor.author Perry, Kaitlyn Anne dc.date.accessioned 2017-03-01T17:40:25Z dc.date.available 2017-03-01T17:40:25Z dc.date.issued 2016 dc.identifier.other u0015_0000001_0002229 dc.identifier.other Perry_alatus_0004D_12680 dc.identifier.uri https://ir.ua.edu/handle/123456789/2587 dc.description Electronic Thesis or Dissertation dc.description.abstract The group of automorphisms of the affine plane has the structure of an amalgamated free product of the triangular and affine subgroups. This leads us to the polydegree: the unique sequence of degrees of the triangular automorphisms in the amalgamated free product decomposition of the automorphism. This group is also endowed with the structure of an infinite dimensional algebraic variety. The interaction between these two structures is not well understood. We use the Valuation Criterion, due to Furter, to study the interaction between these structures; in particular, it allows us to see if an automorphism in G is also in the closure of $G_d$, where d is the polydegree sequence. In this paper, we will discuss a method that gives us new results concerning a class of automorphisms with a polydegree of length one being contained in the closure (in the Zariski topology) of a set of automorphisms with a polydegree of length 2. dc.format.extent 57 p. dc.format.medium electronic dc.format.mimetype application/pdf dc.language English dc.language.iso en_US dc.publisher University of Alabama Libraries dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations dc.relation.ispartof The University of Alabama Libraries Digital Collections dc.relation.hasversion born digital dc.rights All rights reserved by the author unless otherwise indicated. dc.subject.other Mathematics dc.title Polydegree properties of polynomial automorphisms dc.type thesis dc.type text etdms.degree.department University of Alabama. Dept. of Mathematics etdms.degree.discipline Mathematics etdms.degree.grantor The University of Alabama etdms.degree.level doctoral etdms.degree.name Ph.D.
﻿