On the entropy and generators of dynamical systems

Beloslav Riečan

Applications of Mathematics (1996)

  • Volume: 41, Issue: 3, page 161-168
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Riečan, Beloslav. "On the entropy and generators of dynamical systems." Applications of Mathematics 41.3 (1996): 161-168. <http://eudml.org/doc/32943>.

@article{Riečan1996,
abstract = {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.},
author = {Riečan, Beloslav},
journal = {Applications of Mathematics},
keywords = {entropy of dynamical systems; fuzzy partitions; entropy of generating partition; entropy of dynamical systems; fuzzy partitions; entropy of generating partition},
language = {eng},
number = {3},
pages = {161-168},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the entropy and generators of dynamical systems},
url = {http://eudml.org/doc/32943},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Riečan, Beloslav
TI - On the entropy and generators of dynamical systems
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 3
SP - 161
EP - 168
AB - 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.
LA - eng
KW - entropy of dynamical systems; fuzzy partitions; entropy of generating partition; entropy of dynamical systems; fuzzy partitions; entropy of generating partition
UR - http://eudml.org/doc/32943
ER -

References

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  1. Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981. (1981) Zbl0503.68069MR0631231
  2. Ergodic Theory and Information, Willey, New York, 1965. (1965) Zbl0141.16702MR0192027
  3. 10.1016/0022-247X(91)90181-X, J. Math. Anal. Appl. 169 (1991), 111–143. (1991) MR1135265DOI10.1016/0022-247X(91)90181-X
  4. Measure preserving transformation and the entropy of fuzzy partition, 13th Linz seminar on fuzzy set theory (Linz 1991), 25–27. 
  5. 10.1006/jmaa.1993.1220, J. Math. Anal. Appl. 176 (1993), 359–373. (1993) Zbl0782.28012MR1224152DOI10.1006/jmaa.1993.1220
  6. 10.1016/0022-247X(83)90004-5, J. Math. Anal. Appl. 94 (1983), 38–43. (1983) Zbl0511.94030MR0701448DOI10.1016/0022-247X(83)90004-5
  7. On the entropy of dynamical systems, Proc. Ergodic theory and related topics II (Georgenthal 1986), Teubner, Berlin, 1987, 135–138. (1987, 135–138) MR0931138
  8. The entropy of F -quantum spaces, Math. Slovaca 40 (1990), 177–190. (1990) MR1094772
  9. 10.1016/0165-0114(92)90350-D, Fuzzy Sets and Systems 48 (1992), 351–363. (1992) MR1178175DOI10.1016/0165-0114(92)90350-D
  10. 10.1080/03081079108945015, Int. J. General Systems 20 (1990), 67–71. (1990) DOI10.1080/03081079108945015
  11. On a type of entropy of dynamical systems, Tatra Mountains Math. Publications. 
  12. Fundamentals of Measurable Dynamics, Claredon Press, Oxford, 1990. (1990) Zbl0718.28008MR1086631
  13. The entropy of Q - F -dynamical systems, Busefal 48 (1991), 24–26. (1991) 

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