2026/07/29 by A. Blokh, L. Oversteegen, V. Timorin
Mathematics · #math.DS #msc:37F10 #msc:37F20
arxiv created 2026/07/29 · arxiv updated 2026/07/30
Let σ3:\mathbbS→ \mathbbS be the tripling map of the unit circle. For sequences \Li\ of σ3-invariant dendritic laminations we study limits (c, d) of their critical portraits assuming that one such limit P=(c_∘, d_∘) is given. If the endpoints of c_∘ and d_∘ are non-periodic, then there is a unique lamination L with finite critical sets such that c and d can be any couple of critical chords compatible with L. As the extreme opposite case we consider P=(0 \frac13, 0 \frac23) and describe the corresponding countable closed family of possible critical portraits (c, d) and the distinct laminations corresponding to them. These results can be useful for the construction of a model for the cubic connectedness locus.