2,994 research outputs found
Hyperbolic Components in Exponential Parameter Space
We discuss the space of complex exponential maps \Ek\colon z\mapsto
e^{z}+\kappa. We prove that every hyperbolic component has connected
boundary, and there is a conformal isomorphism \Phi_W\colon W\to\half^- which
extends to a homeomorphism of pairs \Phi_W\colon(\ovl
W,W)\to(\ovl\half^-,\half^-). This solves a conjecture of Baker and Rippon,
and of Eremenko and Lyubich, in the affirmative. We also prove a second
conjecture of Eremenko and Lyubich.Comment: To appear in: Comptes Rendues Acad Sci Paris.-- Detailed description
of results can be found in ArXiv math.DS/0311480.-- 6 pages, 1 figur
Meromorphic solutions of higher order Briot-Bouquet differential equations
For differential equations where is a polynomial, we
prove that all meromorphic solutions having at least one pole are elliptic
functions, possibly degenerate
Quasi-exactly solvable quartic: real algebraic spectral locus
We describe the real quasi-exactly solvable spectral locus of the
PT-symmetric quartic using the Nevanlinna parametrization.Comment: 17 pages, 11 figure
Value distribution and potential theory
We describe some results of value distribution theory of holomorphic curves
and quasiregular maps, which are obtained using potential theory. Among the
results discussed are: extensions of Picard's theorems to quasiregular maps
between Riemannian manifolds, a version of the Second Main Theorem of
Nevanlinna for curves in projective space and non-linear divisors, description
of extremal functions in Nevanlinna theory and results related to Cartan's 1928
conjecture on holomorphic curves in the unit disc omitting hyperplanes
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