Geodesic
On the transfer of a number of concepts of statistical radiophysics to the theory of one-dimensional point mappings
Modelirovanie i analiz informacionnyh sistem, Tome 25 (2018) no. 1, pp. 7-17

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

In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback–Leibler entropy in the theory of point mappings is considered. It has been shown that this information-like value is able to describe the behaviour of statistical ensembles of one-dimensional mappings. In the framework of this theory some general properties of its behaviour were found out. Constructivity of the Kullback–Leibler entropy in the theory of point mappings was shown by means of its direct calculation for the “saw tooth” mapping with linear initial probability density. Moreover, for this mapping the denumerable set of initial probability densities hitting into its stationary probability density after a finite number of steps was pointed out.
Keywords: period doubling bifurcation, B-spline, partition of unity.
Mots-clés : discrete Fourier transform, Frobenius–Perron equation 
@article{MAIS_2018_25_1_a1,
     author = {A. M. Agalarov and A. A. Potapov and A. E. Rassadin and A. V. Stepanov},
     title = {On the transfer of a number of concepts of statistical radiophysics to the theory of one-dimensional point mappings},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {7--17},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a1/}
}
TY  - JOUR
AU  - A. M. Agalarov
AU  - A. A. Potapov
AU  - A. E. Rassadin
AU  - A. V. Stepanov
TI  - On the transfer of a number of concepts of statistical radiophysics to the theory of one-dimensional point mappings
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2018
SP  - 7
EP  - 17
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a1/
LA  - ru
ID  - MAIS_2018_25_1_a1
ER  - 
%0 Journal Article
%A A. M. Agalarov
%A A. A. Potapov
%A A. E. Rassadin
%A A. V. Stepanov
%T On the transfer of a number of concepts of statistical radiophysics to the theory of one-dimensional point mappings
%J Modelirovanie i analiz informacionnyh sistem
%D 2018
%P 7-17
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a1/
%G ru
%F MAIS_2018_25_1_a1
A. M. Agalarov; A. A. Potapov; A. E. Rassadin; A. V. Stepanov. On the transfer of a number of concepts of statistical radiophysics to the theory of one-dimensional point mappings. Modelirovanie i analiz informacionnyh sistem, Tome 25 (2018) no. 1, pp. 7-17. http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a1/