Geodesic
On the entropy and generators of dynamical systems
Applications of Mathematics, Tome 41 (1996) no. 3, pp. 161-168

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

DOI MR   Zbl

Recently D. Dumitrescu ([4], [5]) introduced a new kind of entropy of dynamical systems using fuzzy partitions ([1], [6]) instead of usual partitions (see also [7], [11], [12]). In this article a representation theorem is proved expressing the entropy of the dynamical system by the entropy of a generating partition.
Recently D. Dumitrescu ([4], [5]) introduced a new kind of entropy of dynamical systems using fuzzy partitions ([1], [6]) instead of usual partitions (see also [7], [11], [12]). In this article a representation theorem is proved expressing the entropy of the dynamical system by the entropy of a generating partition.
DOI : 10.21136/AM.1996.134319
Classification : 28D20
Keywords: entropy of dynamical systems; fuzzy partitions; entropy of generating partition 
Riečan, Beloslav. On the entropy and generators of dynamical systems. Applications of Mathematics, Tome 41 (1996) no. 3, pp. 161-168. doi: 10.21136/AM.1996.134319
@article{10_21136_AM_1996_134319,
     author = {Rie\v{c}an, Beloslav},
     title = {On the entropy and generators of dynamical systems},
     journal = {Applications of Mathematics},
     pages = {161--168},
     year = {1996},
     volume = {41},
     number = {3},
     doi = {10.21136/AM.1996.134319},
     mrnumber = {1382463},
     zbl = {0863.28014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134319/}
}
TY  - JOUR
AU  - Riečan, Beloslav
TI  - On the entropy and generators of dynamical systems
JO  - Applications of Mathematics
PY  - 1996
SP  - 161
EP  - 168
VL  - 41
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134319/
DO  - 10.21136/AM.1996.134319
LA  - en
ID  - 10_21136_AM_1996_134319
ER  - 
%0 Journal Article
%A Riečan, Beloslav
%T On the entropy and generators of dynamical systems
%J Applications of Mathematics
%D 1996
%P 161-168
%V 41
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1996.134319/
%R 10.21136/AM.1996.134319
%G en
%F 10_21136_AM_1996_134319

[1] J. L. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York, 1981. | MR | Zbl

[2] P. Billingsley: Ergodic Theory and Information. Willey, New York, 1965. | MR | Zbl

[3] D. Butnariu, E. P. Klement: Triangular norm-based measures and their Markov kernel representation. J. Math. Anal. Appl. 169 (1991), 111–143. | DOI | MR

[4] D. Dumitrescu: Measure preserving transformation and the entropy of fuzzy partition. 13th Linz seminar on fuzzy set theory (Linz 1991), 25–27.

[5] D. Dumitrescu: Fuzzy measures and the entropy of fuzzy partitions. J. Math. Anal. Appl. 176 (1993), 359–373. | DOI | MR | Zbl

[6] K. Kuriyama: Entropy of a finite partition of fuzzy sets. J. Math. Anal. Appl. 94 (1983), 38–43. | DOI | MR | Zbl

[7] P. Maličký, B. Riečan: On the entropy of dynamical systems. Proc. Ergodic theory and related topics II (Georgenthal 1986), Teubner, Berlin, 1987, 135–138. | MR

[8] D. Markechová: The entropy of $F$-quantum spaces. Math. Slovaca 40 (1990), 177–190. | MR

[9] D. Markechová: The entropy of fuzzy dynamical systems and generators. Fuzzy Sets and Systems 48 (1992), 351–363. | DOI | MR

[10] R. Mesiar: The Bayes formula and the entropy of fuzzy probability spaces. Int. J. General Systems 20 (1990), 67–71. | DOI

[11] B. Riečan: On a type of entropy of dynamical systems. Tatra Mountains Math. Publications.

[12] D. J. Rudolph: Fundamentals of Measurable Dynamics. Claredon Press, Oxford, 1990. | MR | Zbl

[13] J. Rybárik: The entropy of $Q$-$F$-dynamical systems. Busefal 48 (1991), 24–26.

Cité par Sources :