Geodesic
The spectrum of a perturbation of a hyperbolic toral automorphism
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXII, Tome 411 (2013), pp. 125-134 
A. M. Levin. The spectrum of a perturbation of a hyperbolic toral automorphism. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXII, Tome 411 (2013), pp. 125-134. http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a7/
@article{ZNSL_2013_411_a7,
     author = {A. M. Levin},
     title = {The spectrum of a~perturbation of a~hyperbolic toral automorphism},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--134},
     year = {2013},
     volume = {411},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a7/}
}
TY  - JOUR
AU  - A. M. Levin
TI  - The spectrum of a perturbation of a hyperbolic toral automorphism
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 125
EP  - 134
VL  - 411
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a7/
LA  - ru
ID  - ZNSL_2013_411_a7
ER  - 
%0 Journal Article
%A A. M. Levin
%T The spectrum of a perturbation of a hyperbolic toral automorphism
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 125-134
%V 411
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_411_a7/
%G ru
%F ZNSL_2013_411_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we consider a Markov operator (i.e., a contraction preserving the subspace of constants and the nonnegativity of functions) in the $L^2$ space on the $n$-dimensional torus that is a special perturbation of the unitary operator corresponding to a hyperbolic toral automorphism. We prove some properties of its spectrum and the spectrum of some related operators.

[1] A. M. Vershik, “Polymorphisms, Markov processes, quasi-similarity”, Discrete Contin. Dyn. Syst., 13:5 (2005), 1305–1324 | DOI | MR | Zbl

[2] A. M. Vershik, “Mnogoznachnye otobrazheniya s invariantnoi meroi (polimorfizmy) i markovskie operatory”, Zap. nauchn. semin. LOMI, 72, 1977, 26–61 | MR | Zbl

[3] A. M. Vershik, “Sverkhgrubost giperbolicheskikh avtomorfizmov i unitarnye dilatatsii markovskikh operatorov”, Vestnik LGU, ser. 1, 1987, no. 3, 28–33 | MR | Zbl

[4] P. Khalmosh, Gilbertovo prostranstvo v zadachakh, Moskva, M., 1970