Geodesic
Dense chaos
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 747-752.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

According to A. Lasota, a continuous function $f$ from a real compact interval $I$ into itself is called generically chaotic if the set of all points $(x,y)$, for which $\liminf_{n\to\infty} |f^n(x)-f^n(y)|=0$ and $\limsup_{n\to\infty} |f^n(x)-f^n(y)|>0$, is residual in $I\times I$. Being inspired by this definition we say that $f$ is densely chaotic if this set is dense in $I\times I$. A characterization of the generically chaotic functions is known. In the paper the densely chaotic functions are characterized and it is proved that in the class of piecewise monotone maps with finite number of pieces the notion of dense chaos and that of generic chaos coincide.
Classification : 26A18, 37D45, 54H20, 58F03, 58F13
Keywords: dense chaos; generic chaos; piecewise monotone map 
@article{CMUC_1992__33_4_a20,
     author = {Snoha, L'ubom{\'\i}r},
     title = {Dense chaos},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {747--752},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {1992},
     mrnumber = {1240197},
     zbl = {0784.58043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a20/}
}
TY  - JOUR
AU  - Snoha, L'ubomír
TI  - Dense chaos
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 747
EP  - 752
VL  - 33
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a20/
LA  - en
ID  - CMUC_1992__33_4_a20
ER  - 
%0 Journal Article
%A Snoha, L'ubomír
%T Dense chaos
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 747-752
%V 33
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a20/
%G en
%F CMUC_1992__33_4_a20
Snoha, L'ubomír. Dense chaos. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 747-752. http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a20/