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Nonbasic harmonic maps onto convex wedges

Josephi Cima, Alberti Livingston (1993)

Colloquium Mathematicae

We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation f z ¯ = a f z where a(z) is a nontrivial extreme point of the unit ball of H .

Non-landing hairs in Sierpiński curve Julia sets of transcendental entire maps

Antonio Garijo, Xavier Jarque, Mónica Moreno Rocha (2011)

Fundamenta Mathematicae

We consider the family of transcendental entire maps given by f a ( z ) = a ( z - ( 1 - a ) ) e x p ( z + a ) where a is a complex parameter. Every map has a superattracting fixed point at z = -a and an asymptotic value at z = 0. For a > 1 the Julia set of f a is known to be homeomorphic to the Sierpiński universal curve, thus containing embedded copies of any one-dimensional plane continuum. In this paper we study subcontinua of the Julia set that can be defined in a combinatorial manner. In particular, we show the existence of non-landing...

Nonlinear differential monomials sharing two values

Sujoy Majumder (2016)

Mathematica Bohemica

Using the notion of weighted sharing of values which was introduced by Lahiri (2001), we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely h n h ( k ) ( h = f , ...

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