The paper answers some questions asked by Sharkovski concerning the map F:(u,v) ↦ (u(4-u-v),uv) of the triangle Δ = u,v ≥ 0: u+v ≤ 4. We construct an absolutely continuous σ-finite invariant measure for F. We also prove the following strange phenomenon. The preimages of side I = Δ ∩ v=0 form a dense subset of Δ and there is another dense set Λ consisting of points whose orbits approach the interval I but are not attracted by I.
@article{bwmeta1.element.bwnjournal-article-fmv155i1p45bwm,
author = {Grzegorz \'Swirszcz},
title = {On a certain map of a triangle},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {45-57},
zbl = {0907.58040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv155i1p45bwm}
}
Świrszcz, Grzegorz. On a certain map of a triangle. Fundamenta Mathematicae, Tome 158 (1998) pp. 45-57. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv155i1p45bwm/
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