<< A significant open question in transcendental dynamics asks if it is possible for a point, and thus all points, of a wandering domain to have a bounded orbit. >>
<< In other words, is there a transcendental entire function f with a wandering domain U such that its forward orbit, U_n≥0 f^n(U), is bounded? >>
AA << give a partial answer to this question by constructing an example of a such a wandering domain U which has a nearly bounded orbit; >>
<< In other words, the set of natural numbers n for which f^n(U) is contained in D has upper (and lower) natural density one. >>
<< This is in particularly strong contrast to all existing examples of wandering domains, for which the quantity (..) is equal to zero for any choice of bounded domain D. >>
Leticia Pardo-Simon, David J. Sixsmith. Wandering domains with nearly bounded orbits. arXiv: 2307.16682v1 [math.DS]. Jul 31, 2023.
Also: Unbounded fast escaping wandering domains. https://arxiv.org/abs/2210.13350 ; Escaping sets of continuous functions. https://arxiv.org/abs/1601.04010
Also: 'escape', in FonT: https://flashontrack.blogspot.com/search?q=escape
Also: 'fuga', in Notes (quasi-stochastic poetry): https://inkpi.blogspot.com/search?q=fuga
Keywords: gst, wandering domain, escape