jordan arc
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2017 ◽  
Vol 39 (2) ◽  
pp. 370-391
Author(s):  
JIANXUN FU ◽  
GAOFEI ZHANG

We show that there exist non-landing exponential rays with bounded accumulation sets. By introducing folding models of certain rays, we prove that each of the corresponding accumulation sets is an indecomposable continuum containing part of the ray, an indecomposable continuum disjoint from the ray or a Jordan arc.


2009 ◽  
Vol 52 (1) ◽  
pp. 235-240
Author(s):  
Andreas Sauer

AbstractWe prove that if two transcendental meromorphic functions share all limit values from a set of positive linear measure on a rectifiable Jordan arc, then they share all limit values.


Author(s):  
Hubert de Fraysseix ◽  
Patrice Ossona de Mendez
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1972 ◽  
Vol 72 (2) ◽  
pp. 205-207 ◽  
Author(s):  
D. G. Larman ◽  
P. McMullen

Let f:[0, 1]→R2 be a Jordan arc, and for t, u ∈ [0, 1] let d(t, u) = d(f(t), f(u)) denote the Euclidean length of the chord between f(t) and f(u), and l(t, u) = l(f(t), f(u)) the corresponding arc-length, when this is defined. We say that f has the increasing chord property if d(t2, t3) ≤ d(t1, t4) whenever 0 ≤ t1 ≤ t2 ≤ t3 ≤ t4 ≤ 1. In connexion with a problem in complex analysis, K. Binmore has asked (private communication, see (1)) whether there exists an absolute constant K such that.


1970 ◽  
Vol 40 ◽  
pp. 213-220 ◽  
Author(s):  
Charles L. Belna

Let D and C denote the open unit disk and the unit circle in the complex plane, respectively; and let f be a function from D into the Riemann sphere Ω. An arc γ⊂D is said to be an arc at p∈C if γ∪{p} is a Jordan arc; and, for each t (0<t<1), the component of γ∩{z: t≤|z|<1} which has p as a limit point is said to be a terminal subarc of γ. If γ is an arc at p, the arc-cluster set C(f, p,γ) is the set of all points a∈Ω for which there exists a sequence {zk}a⊂γ with zk→p and f(zk)→a.


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