Dynamical Varieties
dc.contributor.author | Stoll, Danny | |
dc.date.accessioned | 2024-05-22T17:28:11Z | |
dc.date.available | 2024-05-22T17:28:11Z | |
dc.date.issued | 2024 | |
dc.date.submitted | 2024 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/193432 | |
dc.description.abstract | The 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.iso | en_US | |
dc.subject | complex dynamics | |
dc.subject | marked cycle | |
dc.subject | monodromy | |
dc.title | Dynamical Varieties | |
dc.type | Thesis | |
dc.description.thesisdegreename | PhD | |
dc.description.thesisdegreediscipline | Mathematics | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.contributor.committeemember | Koch, Sarah Colleen | |
dc.contributor.committeemember | Bansal, Nikhil | |
dc.contributor.committeemember | Hubbard, John H | |
dc.contributor.committeemember | Spatzier, Ralf J | |
dc.contributor.committeemember | Tiozzo, Giulio | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbtoplevel | Science | |
dc.contributor.affiliationumcampus | Ann Arbor | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/193432/1/dastoll_1.pdf | |
dc.identifier.doi | https://dx.doi.org/10.7302/23077 | |
dc.identifier.orcid | 0000-0003-1259-6262 | |
dc.identifier.name-orcid | Stoll, Daniel; 0000-0003-1259-6262 | en_US |
dc.working.doi | 10.7302/23077 | en |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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