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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
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
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
Linking options:
https://www.mathnet.ru/eng/faa199https://doi.org/10.4213/faa199 https://www.mathnet.ru/eng/faa/v36/i3/p1
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