In MSE I've started a discussion providing also some pictures on the properties of shapes of the orbits 0 \to 1 \to b \to b^b \to ... and in which way there occurs "divergence". Such "divergence" has been proven for classes of bases b on boundary of the Shell-Thron-region by I.N.Baker & Rippon in 1983 and according to Sheldonison has been thoroughly investigated by J.C.Yoccoz .

See here: https://math.stackexchange.com/q/3323851

Possibly I can take some pictures here, but the transfer of the mathjax-formulae is a visual horror for me... Conclusions I might transfer to this place if the discussion has some sufficient finishing.

Gottfried

Additional material:

http://go.helms-net.de/math/tetdocs/_equ...quator.pdf an earlier article of mine as first approximation to the problem

https://math.stackexchange.com/q/1820410/1714

https://math.stackexchange.com/questions...it-chaotic

See here: https://math.stackexchange.com/q/3323851

Possibly I can take some pictures here, but the transfer of the mathjax-formulae is a visual horror for me... Conclusions I might transfer to this place if the discussion has some sufficient finishing.

Gottfried

Additional material:

http://go.helms-net.de/math/tetdocs/_equ...quator.pdf an earlier article of mine as first approximation to the problem

https://math.stackexchange.com/q/1820410/1714

https://math.stackexchange.com/questions...it-chaotic

Gottfried Helms, Kassel