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Dynamical Varieties

dc.contributor.authorStoll, Danny
dc.date.accessioned2024-05-22T17:28:11Z
dc.date.available2024-05-22T17:28:11Z
dc.date.issued2024
dc.date.submitted2024
dc.identifier.urihttps://hdl.handle.net/2027.42/193432
dc.description.abstractThe locus of periodic cycles is of fundamental importance to any discrete time dynamical system. We introduce a family Cyc_p(F) of marked cycle varieties that parameterize the $p$-cycles of an algebraic family of dynamical systems. We describe a dynamically natural cell structure for marked cycle curves over the moduli space Per(1) of quadratic polynomials and over the moduli space Per(2) of quadratic rational maps with a 2-periodic critical point. We then analyze the combinatorics of the resulting cell structures, obtaining formulas for the number of cells of each dimension.
dc.language.isoen_US
dc.subjectcomplex dynamics
dc.subjectmarked cycle
dc.subjectmonodromy
dc.titleDynamical Varieties
dc.typeThesis
dc.description.thesisdegreenamePhD
dc.description.thesisdegreedisciplineMathematics
dc.description.thesisdegreegrantorUniversity of Michigan, Horace H. Rackham School of Graduate Studies
dc.contributor.committeememberKoch, Sarah Colleen
dc.contributor.committeememberBansal, Nikhil
dc.contributor.committeememberHubbard, John H
dc.contributor.committeememberSpatzier, Ralf J
dc.contributor.committeememberTiozzo, Giulio
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbtoplevelScience
dc.contributor.affiliationumcampusAnn Arbor
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/193432/1/dastoll_1.pdf
dc.identifier.doihttps://dx.doi.org/10.7302/23077
dc.identifier.orcid0000-0003-1259-6262
dc.identifier.name-orcidStoll, Daniel; 0000-0003-1259-6262en_US
dc.working.doi10.7302/23077en
dc.owningcollnameDissertations and Theses (Ph.D. and Master's)


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