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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 3, Pages 1–8
DOI: https://doi.org/10.4213/faa199 (Mi faa199) 		 
This article is cited in 9 scientific papers (total in 10 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
Full-text PDF (130 kB) Citations (10)
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DOI: https://doi.org/10.4213/faa199
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.
Received: 07.05.2002
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 3, Pages 165–171
DOI: https://doi.org/10.1023/A:1020107203200
Bibliographic databases:
Document Type: Article
UDC: 517.938+512.7
Language: Russian
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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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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