On a certain map of a triangle

• Autorzy: Grzegorz Świrszcz
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 1
• Strony: 45-57

Daty

wydano

1998

otrzymano

1996-11-07

poprawiono

1997-05-12

Twórcy

autor

Grzegorz Świrszcz

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Basel, 1980.
• [2] A. Douady et J. Hubbard, Itération des polynômes quadratiques complexes, C. R. Acad. Sci. Paris 294 (1982), 123-126.
• [3] R. Lozi, Un attracteur étrange du type attracteur de Hénon, J. Phys. 39 (1978), suppl. au no. 8, 9-10.