# On a certain map of a triangle

Fundamenta Mathematicae (1998)

- Volume: 155, Issue: 1, page 45-57
- ISSN: 0016-2736

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topŚwirszcz, Grzegorz. "On a certain map of a triangle." Fundamenta Mathematicae 155.1 (1998): 45-57. <http://eudml.org/doc/212242>.

@article{Świrszcz1998,

abstract = {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.},

author = {Świrszcz, Grzegorz},

journal = {Fundamenta Mathematicae},

keywords = {non-hyperbolic dynamical systems; invariant measure; attractors},

language = {eng},

number = {1},

pages = {45-57},

title = {On a certain map of a triangle},

url = {http://eudml.org/doc/212242},

volume = {155},

year = {1998},

}

TY - JOUR

AU - Świrszcz, Grzegorz

TI - On a certain map of a triangle

JO - Fundamenta Mathematicae

PY - 1998

VL - 155

IS - 1

SP - 45

EP - 57

AB - 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.

LA - eng

KW - non-hyperbolic dynamical systems; invariant measure; attractors

UR - http://eudml.org/doc/212242

ER -

## References

top- [1] P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Basel, 1980. Zbl0458.58002
- [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.