Geodesic
Sharkovskiĭ's theorem holds for some discontinuous functions
Piotr Szuca1
1 Department of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland
Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 27-41.

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

We show that the Sharkovski{ĭ} ordering of periods of a continuous real function is also valid for every function with connected $G_\delta $ graph. In particular, it is valid for every ${\rm DB}_1$ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected $G_\delta $ graph.
DOI : 10.4064/fm179-1-3
Keywords: sharkovski ordering periods continuous real function valid every function connected delta graph particular valid every function therefore every derivative tool apply itinerary lemma functions connected delta graph

Piotr Szuca 1

1 Department of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland 
@article{10_4064_fm179_1_3,
     author = {Piotr Szuca},
     title = {Sharkovski\u{i}'s theorem holds for some
 discontinuous functions},
     journal = {Fundamenta Mathematicae},
     pages = {27--41},
     publisher = {mathdoc},
     volume = {179},
     number = {1},
     year = {2003},
     doi = {10.4064/fm179-1-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm179-1-3/}
}
TY  - JOUR
AU  - Piotr Szuca
TI  - Sharkovskiĭ's theorem holds for some
 discontinuous functions
JO  - Fundamenta Mathematicae
PY  - 2003
SP  - 27
EP  - 41
VL  - 179
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm179-1-3/
DO  - 10.4064/fm179-1-3
LA  - en
ID  - 10_4064_fm179_1_3
ER  - 
%0 Journal Article
%A Piotr Szuca
%T Sharkovskiĭ's theorem holds for some
 discontinuous functions
%J Fundamenta Mathematicae
%D 2003
%P 27-41
%V 179
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm179-1-3/
%R 10.4064/fm179-1-3
%G en
%F 10_4064_fm179_1_3
Piotr Szuca. Sharkovskiĭ's theorem holds for some
 discontinuous functions. Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 27-41. doi : 10.4064/fm179-1-3. http://geodesic.mathdoc.fr/articles/10.4064/fm179-1-3/

Cité par Sources :