This thesis is devoted to the study of foliations that come from dynamical systems.
In the first part we study foliations of Stein manifolds locally given by vector fields. The leaves of such foliations are Riemann surfaces. We prove that for a generic foliation all leaves except for not more than a countable number are homeomorphic to disks, the rest are homeomorphic to cylinders. We also prove that a generic foliation is complex Kupka-Smale.
In the second part of the thesis we study complex H\'non maps. The sets of points $U^+$ and $U^-$ that have unbounded forward and backwards orbits correspondingly, is naturally endowed with holomorphic foliations $^+$ and $^-$. We describe the critical locus -- the set of tangencies between these foliations -- for H\'{e}non maps that are small perturbations of quadratic polynomials with disconnected Julia set.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/26148 |
| Date | 15 February 2011 |
| Creators | Firsova, Tatiana |
| Contributors | Khovanskii, Askold |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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