Algebraic and geometric dynamics in several complex variables.
dc.contributor.author | Dabija, Marius Viorel | |
dc.contributor.advisor | Fornaess, John Erik | |
dc.date.accessioned | 2016-08-30T18:07:08Z | |
dc.date.available | 2016-08-30T18:07:08Z | |
dc.date.issued | 2000 | |
dc.identifier.uri | http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:9977140 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/132552 | |
dc.description.abstract | We discuss various algebraic, geometric and dynamical properties of the holomorphic self-maps of complex projective manifolds. <italic>Self-maps of</italic> <blkbd>P2</blkbd> <italic>with invariant elliptic curves</italic>. If a regular self-map of <blkbd>P2</blkbd> leaves invariant an elliptic plane curve <italic>C</italic>, the closure of the backward orbit of any point on <italic>C</italic> equals the Julia set. For smooth cubics, two types of self-maps are discussed: tangent processes, and elementary maps. For singular elliptic curves, invariants are defined at the singular points, and calculated for several families of curves: duals of smooth cubics, and elliptic quartics with two singular points. <italic>Self-maps of ruled surfaces</italic>. We give a systematic description of the self-maps of ruled surfaces. The discussion is based on the rigidity of the curves with negative or zero self-intersection. The configurations of completely invariant curves is listed, and an application to the dynamics of elementary maps of <blkbd>P2</blkbd> is deduced. <italic>Completely invariant hypersurfaces in projective spaces</italic>. We discuss the structure of those hypersurfaces that are completely invariant for some rational self-map of <blkbd>Pn</blkbd> . This involves the study of essential hypersurfaces, Bottcher divisors, degenerate essential components and stars. <italic>Self-maps of projective bundles</italic>. Given a self-map of a projective bundle over <blkbd>Pn</blkbd> , we study its geometry (fiber-degree, algebraic degree, lifting to the dual vector bundle) and its dynamics (Green function, Fatou components, Julia set). | |
dc.format.extent | 160 p. | |
dc.language | English | |
dc.language.iso | EN | |
dc.subject | Algebraic | |
dc.subject | Complex Variables | |
dc.subject | Geometric Dynamics | |
dc.subject | Holomorphic | |
dc.subject | Hypersurfaces | |
dc.subject | Invariant Elliptic Curves | |
dc.subject | Ruled Surfaces | |
dc.subject | Several | |
dc.title | Algebraic and geometric dynamics in several complex variables. | |
dc.type | Thesis | |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Mathematics | |
dc.description.thesisdegreediscipline | Pure Sciences | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/132552/2/9977140.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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