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 Mat. Sb., 1999, Volume 190, Number 1, Pages 3–28 (Mi msb376)

The spectral multiplicity function and geometric representations of interval exchange transformations

O. N. Ageev

N. E. Bauman Moscow State Technical University

Abstract: The article solves the problem of which sets can be the set $\mathscr M$ of values of the spectral multiplicity function of an ergodic (strictly ergodic) interval exchange transformation and also of a simply ergodic dynamical system. By means of the method of geometric representations subsets of transformations are constructed that are generic in the metric and topological sense in the respective subclasses, and whose spectral multiplicity function has a prescribed set of values (in $\mathbb N\cup\{\infty\}$ naturally). These classes of transformations exhibit a new spectral effect: the component of multiplicity 1 in the spectrum is not the same as the spectrum of any factor of these transformations. Specific examples of strictly ergodic interval exchange transformations are constructed whose spectral multiplicity functions have all possible sets of values.

DOI: https://doi.org/10.4213/sm376

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English version:
Sbornik: Mathematics, 1999, 190:1, 1–28

Bibliographic databases:

UDC: 517.9
MSC: Primary 28D05, 47A35; Secondary 11K50

Citation: O. N. Ageev, “The spectral multiplicity function and geometric representations of interval exchange transformations”, Mat. Sb., 190:1 (1999), 3–28; Sb. Math., 190:1 (1999), 1–28

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb376
• https://doi.org/10.4213/sm376
• http://mi.mathnet.ru/eng/msb/v190/i1/p3

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This publication is cited in the following articles:
1. Ageev O.N., “On asymmetry of the future and the past for limit self-joinings”, Proc. Amer. Math. Soc., 131:7 (2003), 2053–2062
2. ALEXANDRE I. DANILENKO, “A survey on spectral multiplicities of ergodic actions”, Ergod. Th. Dynam. Sys, 2011, 1
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