On the Existence of Attracting Domains for Maps Tangent to the Identity.

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dc.contributor.author Lapan, Sara W. en_US
dc.date.accessioned 2013-09-24T16:03:53Z
dc.date.available NO_RESTRICTION en_US
dc.date.available 2013-09-24T16:03:53Z
dc.date.issued 2013 en_US
dc.date.submitted 2013 en_US
dc.identifier.uri http://hdl.handle.net/2027.42/100070
dc.description.abstract The main result we discuss is for germs of holomorphic self-maps in two complex variables that have a unique characteristic direction and this direction is non-degenerate. We prove that there exists a domain of attraction whose points converge to the origin along the characteristic direction and on which the map is conjugate to translation. In the case of a global automorphism, the corresponding invariant attracting domain is a Fatou-Bieberbach domain. In addition, we discuss other types of germs of holomorphic self-maps in two or more complex variables that fix the origin, in each case determining whether or not there exists an invariant attracting domain whose points converge to the origin tangentially to the same direction. en_US
dc.language.iso en_US en_US
dc.subject Complex Dynamics en_US
dc.subject Holomorphic Dynamics en_US
dc.subject Complex Analysis en_US
dc.subject Dynamical Systems en_US
dc.subject Characteristic Direction en_US
dc.subject Domain of Attraction en_US
dc.title On the Existence of Attracting Domains for Maps Tangent to the Identity. en_US
dc.type Thesis en_US
dc.description.thesisdegreename PhD en_US
dc.description.thesisdegreediscipline Mathematics en_US
dc.description.thesisdegreegrantor University of Michigan, Horace H. Rackham School of Graduate Studies en_US
dc.contributor.committeemember Jonsson, Mattias en_US
dc.contributor.committeemember Mesa, Vilma M. en_US
dc.contributor.committeemember Barrett, David E. en_US
dc.contributor.committeemember Clark, Trevor en_US
dc.contributor.committeemember Grundmeier, Dusty E. en_US
dc.subject.hlbsecondlevel Mathematics en_US
dc.subject.hlbtoplevel Science en_US
dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/100070/1/swlapan_1.pdf
dc.owningcollname Dissertations and Theses (Ph.D. and Master's)
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