On the set of continuity of topological entropy families of segment mappings depending on the parameter
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 42-50.

Voir la notice de l'article provenant de la source Math-Net.Ru

Families of continuous mappings of the interval continuously depending on a parameter are considered. Any $G_\delta$ set dense in the parameter space is realized as the set of continuity of topological entropy for a suitable family of continuous mappings.
Keywords: dynamical system, topological entropy.
@article{FAA_2021_55_3_a2,
     author = {A. N. Vetokhin},
     title = {On the set of continuity of topological entropy families of segment mappings depending on the parameter},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {42--50},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a2/}
}
TY  - JOUR
AU  - A. N. Vetokhin
TI  - On the set of continuity of topological entropy families of segment mappings depending on the parameter
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2021
SP  - 42
EP  - 50
VL  - 55
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a2/
LA  - ru
ID  - FAA_2021_55_3_a2
ER  - 
%0 Journal Article
%A A. N. Vetokhin
%T On the set of continuity of topological entropy families of segment mappings depending on the parameter
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2021
%P 42-50
%V 55
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a2/
%G ru
%F FAA_2021_55_3_a2
A. N. Vetokhin. On the set of continuity of topological entropy families of segment mappings depending on the parameter. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 42-50. http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a2/

[1] R. L. Adler, A. G. Konheim, M. H. McAndrew, “Topological entropy”, Trans. Amer. Math. Soc., 114 (1965), 309–319 | DOI | MR | Zbl

[2] A. B. Katok, B. Khasselblat, Vvedenie v sovremennuyu teoriyu dinamicheskikh sistem, Faktorial, M., 1999

[3] A. N. Vetokhin, “Tipichnoe svoistvo topologicheskoi entropii nepreryvnykh otobrazhenii kompaktov”, Differents. uravneniya, 53:4 (2017), 448–453 | DOI | MR | Zbl

[4] A. N. Vetokhin, “Stroenie mnozhestv tochek polunepreryvnosti topologicheskoi entropii dinamicheskikh sistem, nepreryvno zavisyaschikh ot parametra”, Vestnik Mosk. un-ta. Ser. 1. Matem., mekh., 2019, no. 3, 69–72 | MR

[5] A. N. Vetokhin, “O nekotorykh svoistvakh topologicheskoi entropii i topologicheskogo davleniya semeistv dinamicheskikh sistem, nepreryvno zavisyaschikh ot parametra”, Differents. uravneniya, 55:10 (2019), 1319–1327 | DOI | MR | Zbl

[6] M. Misiurewicz, “Horseshoes for mappings of the interval”, Bull. Acad. Polon. Sci., Ser. Math. Astron. et Phys., 27:2 (1979), 167–169 | MR | Zbl

[7] F. Khausdorf, Teoriya mnozhestv, ONTI, M.-L., 1937

[8] L. Block, “Noncontinuity of topological entropy of maps of the Cantor set and of the interval”, Proc. Amer. Math. Soc., 50 (1975), 388–393 | DOI | MR | Zbl

[9] K. Kuratovskii, Topologiya, v. 1, Mir, M., 1966

[10] M. Misiurewicz, W. Szlenk, “Entropy of piecewise monotone mappings”, Studia Math., 67:1 (1980), 45–63 | DOI | MR | Zbl