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dc.contributor.advisorMcMullen, Curtis T.
dc.contributor.advisorAuroux, Denis
dc.contributor.advisorKahn, Jeremy
dc.contributor.authorLuo, Yusheng
dc.date.accessioned2019-12-12T09:21:51Z
dc.date.created2019-05
dc.date.issued2019-05-14
dc.date.submitted2019
dc.identifier.citationLuo, Yusheng. 2019. Trees, Berkovich Spaces and the Barycentric Extension in Complex Dynamics. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:42029785*
dc.description.abstractA metric space T is called an R-tree if any two points x, y ∈ T can be connected by a unique topological arc [x, y] ⊂ T which is isometric to an interval in R. R-trees are natural generalizations to finite trees and simplicial trees, and have many applications in mapping class groups, Teichmüller theory, hyperbolic 3-manifold and Kleinian groups and etc. In this work, we will give a new construction of R-trees in complex dynamics using barycentric extensions. We will establish the relation between the barycentric construction and the Berkovich construction via the complexified Robison’s field. As an application, we will also use our construction to classify all hyperbolic components that admits degenerating sequences with bounded multipliers.
dc.description.sponsorshipMathematics
dc.format.mimetypeapplication/pdf
dc.language.isoen
dash.licenseLAA
dc.subjectComplex dynamics, hyperbolic geometry, Berkovich spaces, trees
dc.titleTrees, Berkovich Spaces and the Barycentric Extension in Complex Dynamics
dc.typeThesis or Dissertation
dash.depositing.authorLuo, Yusheng
dc.date.available2019-12-12T09:21:51Z
thesis.degree.date2019
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.levelDoctoral
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
thesis.degree.nameDoctor of Philosophy
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.departmentMathematics
dash.identifier.vireo
dash.author.emailyusheng.s.luo@gmail.com


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