Mixing flows with homogeneous spectrum of multiplicity~$2$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 191-197.

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

The paper is devoted to the problem of realization of spectral multiplicities for mixing dynamical systems. It is shown that in the class of mixing flows the homogeneous spectrum of multiplicity $2$ can be realized.
@article{FPM_2016_21_5_a8,
     author = {V. V. Ryzhikov and A. E. Troitskaya},
     title = {Mixing flows with homogeneous spectrum of multiplicity~$2$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {191--197},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a8/}
}
TY  - JOUR
AU  - V. V. Ryzhikov
AU  - A. E. Troitskaya
TI  - Mixing flows with homogeneous spectrum of multiplicity~$2$
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2016
SP  - 191
EP  - 197
VL  - 21
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a8/
LA  - ru
ID  - FPM_2016_21_5_a8
ER  - 
%0 Journal Article
%A V. V. Ryzhikov
%A A. E. Troitskaya
%T Mixing flows with homogeneous spectrum of multiplicity~$2$
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2016
%P 191-197
%V 21
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a8/
%G ru
%F FPM_2016_21_5_a8
V. V. Ryzhikov; A. E. Troitskaya. Mixing flows with homogeneous spectrum of multiplicity~$2$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 191-197. http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a8/

[1] Konev R. A., Ryzhikov V. V., “O nabore spektralnykh kratnostei $\{2, 4,\ldots, 2^n\}$ dlya vpolne ergodicheskikh $\Z^2$-deistvii”, Matem. zametki, 96:3 (2014), 383–392 | DOI | MR | Zbl

[2] Oseledets V. I., “Avtomorfizm s prostym i nepreryvnym spektrom bez gruppovogo svoistva”, Matem. zametki, 5:3 (1969), 323–326 | Zbl

[3] Ryzhikov V. V., “O spektralnykh i peremeshivayuschikh svoistvakh konstruktsii ranga $1$ v ergodicheskoi teorii”, Dokl. RAN, 409:4 (2006), 448–450 | MR | Zbl

[4] Ryzhikov V. V., “Slabye predely stepenei, prostoi spektr simmetricheskikh proizvedenii i peremeshivayuschie konstruktsii ranga $1$”, Matem. sb., 198:5 (2007), 137–159 | DOI | MR | Zbl

[5] Stepin A. M., “Spektralnye svoistva tipichnykh dinamicheskikh sistem”, Izv. AN SSSR. Ser. matem., 50:4 (1986), 801–834 | MR

[6] Tikhonov S. V., “Peremeshivayuschie preobrazovaniya s odnorodnym spektrom”, Matem. sb., 202:8 (2011), 139–160 | DOI | Zbl

[7] Adams T. M., “Smorodinsky's conjecture on rank-one mixing”, Proc. Am. Math. Soc., 126:3 (1998), 739–744 | DOI | MR | Zbl

[8] Ageev O. N., “On ergodic transformations with homogeneous spectrum”, J. Dynam. Control Systems, 5:1 (1999), 149–152 | DOI | MR | Zbl

[9] Danilenko A. I., “A survey on spectral multiplicities of ergodic actions”, Ergodic Theory Dynam. Systems, 33:1 (2013), 81–117 | DOI | MR | Zbl

[10] Danilenko A. I., Ryzhikov V. V., “On self-similarities of ergodic flows”, Proc. London Math. Soc. (3), 104:3 (2012), 431–454 | DOI | MR | Zbl

[11] Katok A., Lemanczyk M., “Some new cases of realization of spectral multiplicity function for ergodic transformations”, Fund. Math., 206 (2009), 185–215 | DOI | MR | Zbl

[12] Ryzhikov V. V., “Transformations having homogeneous spectra”, J. Dynam. Control Systems, 5:1 (1999), 145–148 | DOI | MR | Zbl