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Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 3, Pages 1–8 (Mi faa199)  

This article is cited in 2 scientific papers (total in 3 papers)

The Longest Curves of Given Degree and the Quasicrystallic Harnack Theorem in Pseudoperiodic Topology

V. I. Arnol'dab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Université Paris-Dauphine

Abstract: Upper bounds for ergodic averages of topological characteristics of pseudoperiodic functions and manifolds are found in terms of the degrees of trigonometric polynomials defining these functions and manifolds. The bounds are based on finding the longest trigonometric and spherical curves of a fixed degree.

Keywords: Betti numbers, ergodic theory, characteristic numbers, perihelion, quasicrystalls, Sturm theory, Morse theory

DOI: https://doi.org/10.4213/faa199

Full text: PDF file (130 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2002, 36:3, 165–171

Bibliographic databases:

UDC: 517.938+512.7
Received: 07.05.2002

Citation: V. I. Arnol'd, “The Longest Curves of Given Degree and the Quasicrystallic Harnack Theorem in Pseudoperiodic Topology”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 1–8; Funct. Anal. Appl., 36:3 (2002), 165–171

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. Soprunova, “Zeros of systems of exponential sums and trigonometric polynomials”, Mosc. Math. J., 6:1 (2006), 153–168  mathnet  crossref  mathscinet  zmath
    2. Ulanovskii, A, “The Sturm-Hurwitz theorem and its extensions”, Journal of Fourier Analysis and Applications, 12:6 (2006), 629  crossref  mathscinet  zmath  isi  scopus
    3. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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