Geodesic
On a certain map of a triangle
Fundamenta Mathematicae, Tome 155 (1998) no. 1, pp. 45-57

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $∪F^{-n}(I)$ of Δ and there is another dense set Λ consisting of points whose orbits approach the interval I but are not attracted by I.
DOI : 10.4064/fm-155-1-45-57

Grzegorz Świrszcz 1

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Grzegorz Świrszcz. On a certain map of a triangle. Fundamenta Mathematicae, Tome 155 (1998) no. 1, pp. 45-57. doi: 10.4064/fm-155-1-45-57

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