ARITHMETIC DYNAMICS OF QUADRATIC POLYNOMIALS AND DYNAMICAL UNITS

dc.contributor.advisor	Washington, Lawrence C.	en_US
dc.contributor.author	Panraksa, Chatchawan	en_US
dc.contributor.department	Mathematics	en_US
dc.contributor.publisher	Digital Repository at the University of Maryland	en_US
dc.contributor.publisher	University of Maryland (College Park, Md.)	en_US
dc.date.accessioned	2011-10-08T05:55:31Z
dc.date.available	2011-10-08T05:55:31Z
dc.date.issued	2011	en_US
dc.description.abstract	The arithmetic dynamics of rational functions have been studied in many contexts. In this thesis, we concentrate on periodic points. For \phi(x)=x^2+c with c rational, we give a parametrization of all points of order 4 in quadratic fields. For a point of order two and a point of order three for a rational function defined over a number field with good reduction outside a set S, it is known that the bilinear form B([x_1, y_1], [x_2, y_2]) = x_1y_2 - x_2y_1 yields a unit in the ring of S-integers of a number field. We prove that this is essentially the only bilinear form with this property. Finally, we give restrictions on the orders of rational periodic points for rational functions with everywhere good reduction.	en_US
dc.identifier.uri	http://hdl.handle.net/1903/11942
dc.subject.pqcontrolled	Mathematics	en_US
dc.title	ARITHMETIC DYNAMICS OF QUADRATIC POLYNOMIALS AND DYNAMICAL UNITS	en_US
dc.type	Dissertation	en_US

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