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Funktsional'nyi Analiz i ego Prilozheniya, 2021, Volume 55, Issue 4, Pages 3–21
DOI: https://doi.org/10.4213/faa3854 (Mi faa3854) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture

A. Álvareza, J. L. Bravoa, C. Christopherb, P. Mardešićcd

a Department of Mathematics, University of Extremadura
b School of Engineering, Computing and Mathematics, University of Plymouth
c Université de Bourgogne, Institut de Mathématiques de Bourgogne, Faculté des Sciences Mirande
d University of Zagreb, Department of Mathematics
Full-text PDF (663 kB) Citations (2)
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DOI: https://doi.org/10.4213/faa3854
Abstract: We study the analog of the classical infinitesimal center problem in the plane, but for zero cycles. We define the displacement function in this context and prove that it is identically zero if and only if the deformation has a composition factor. That is, we prove that here the composition conjecture is true, in contrast with the tangential center problem on zero cycles. Finally, we give examples of applications of our results.
Keywords: infinitesimal center, tangential center, Abelian integral, composition conjecture, monodromy.
Funding agency Grant number
Junta de Extremadura IB18023
GR18001
GR18023
Ministerio de Economía y Competitividad MTM2017-83568-P
Croatian Science Foundation PZS-2019-02-3055
Agence Nationale de la Recherche ANR-17-EURE-0002
Received: 04.11.2020
Revised: 05.05.2021
Accepted: 26.05.2021
English version:
Functional Analysis and Its Applications, 2021, Volume 55, Issue 4, Pages 257–271
DOI: https://doi.org/10.1134/S0016266321040018
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. Álvarez, J. L. Bravo, C. Christopher, P. Mardešić, “Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture”, Funktsional. Anal. i Prilozhen., 55:4 (2021), 3–21; Funct. Anal. Appl., 55:4 (2021), 257–271
Citation in format AMSBIB
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\paper Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture
\jour Funktsional. Anal. i Prilozhen.
\yr 2021
\vol 55
\issue 4
\pages 3--21
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\crossref{https://doi.org/10.4213/faa3854}
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\jour Funct. Anal. Appl.
\yr 2021
\vol 55
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\pages 257--271
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Linking options:
  • https://www.mathnet.ru/eng/faa3854
  • https://doi.org/10.4213/faa3854
  • https://www.mathnet.ru/eng/faa/v55/i4/p3
    • This publication is cited in the following 2 articles:
    1. J.L. Bravo, P. Mardešić, D. Novikov, J. Pontigo-Herrera, “Infinitesimal and tangential 16-th Hilbert problem on zero-cycles”, Bulletin des Sciences Mathématiques, 2025, 103634  crossref
    2. V. T. Borukhov, “Algebraic criterion for the existence of a center at a monodromic singular point of a polynomial Liénard system”, Diff. Equat., 58:8 (2022), 1008  crossref
    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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