Exceptional Points in Arithmetic Dynamics

dc.contributor.author	Thompson, Bianca
dc.date.accessioned	2017-12-18T21:15:13Z
dc.date.available	2017-12-18T21:15:13Z
dc.date.issued	2015-05
dc.description.abstract	Let be a morphism of PN defined over a field K. We prove three main results: When K is a number field, we prove that there is a bound B depending only on such that every twist of has no more than B K-rational preperiodic points. (This result is analagous to a result of Silverman for abelian varieties.) For two specific families of quadratic rational maps over Q, we find the bound B explicitly. When K is a finite field, we find the limiting proportion of periodic points in towers of finite fields for polynomial maps associated to algebraic groups, namely pure power maps (z) = zd and Chebyshev polynomials. When K is a number field or Qp for p 6= 3; and L=K is an extension we prove that K fails to be critically reducible at 3. Meanwhile, Q3 is critically reducible at 3.
dc.description.degree	Ph.D.
dc.identifier.uri	http://hdl.handle.net/10125/51024
dc.language	eng
dc.publisher	University of Hawaii at Manoa
dc.relation	Theses for the degree of Doctor of Philosophy (University of Hawaii at Manoa). Math
dc.title	Exceptional Points in Arithmetic Dynamics
dc.type	Thesis
dc.type.dcmi	Text

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