4 papers
Holomorphic Explosions
Aslı Deniz, Carsten Lunde Petersen
This paper concerns the problem of extending the parameter domain of holomorphic motions to include isolated boundary points, punctures of the domains. Supposing that the parameter…
A Converse Landing Theorem in Parameter Spaces
Asli Deniz
In this article, we prove that for several one-dimensional holomorphic families of holomorphic maps, in the parameter plane, there exists a local piece of a curve that lands at a g…
Convergence of Rays with Rational Argument in Hyperbolic Components
Aslı Deniz
In this paper, we use the Carathéodory Convergence Theory to prove a landing theorem of rays in hyperbolic components with rational arguments. Although the proof is done in the set…
A Landing Theorem for Periodic Dynamic Rays for Transcendental Entire Maps with Bounded Post-Singular Set
Aslı Deniz
In this article, we present a landing theorem for periodic dynamic rays for transcendental entire maps which have bounded post-singular sets, by using standard hyperbolic geometry…