Geodesic
Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 4, pp. 3-21

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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
Mots-clés : composition conjecture, monodromy. 
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     author = {A. \'Alvarez and J. L. Bravo and C. Christopher and P. Marde\v{s}i\'c},
     title = {Infinitesimal {Center} {Problem} on {Zero} {Cycles} and the {Composition} {Conjecture}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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A. Álvarez; J. L. Bravo; C. Christopher; P. Mardešić. Infinitesimal Center Problem on Zero Cycles and the Composition Conjecture. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 4, pp. 3-21. http://geodesic.mathdoc.fr/item/FAA_2021_55_4_a0/