@article{fa81d327f8d642aaa53f7d380db6ecc2,
title = "Bifurcations of Zeros in Translated Families of Functions and Applications",
abstract = "In this paper, we study the creation of zeros in a certain type of families of functions. The families studied are given by the difference of two basic functions with a translation made in the argument of one of these functions. The problem is motivated by applications in the 16th Hilbert problem and its ramifications. Here, we apply the results obtained to the study of bifurcations of critical periods in the Loud family of quadratic centers.",
keywords = "Bifurcations, Centers, Critical period, Cyclicity",
author = "P. Marde{\v s}i{\'c} and D. Mar{\'i}n and J. Villadelprat",
note = "Funding Information: P. Marde{\v s}i{\'c} is supported by Croatian Science Foundation (HRZZ) grant PZS-2019-02-3055 from Research Cooperability funded by the European Social Fund and by EIPHI Graduate School (contract ANR-17-EURE-0002). D. Mar{\'i}n is supported by the Ministry of Science, Innovation and Universities of Spain through the grants MTM2015-66165-P and PGC2018-095998-B-I00, by the Agency for Management of University and Research Grants of Catalonia through the grant 2017SGR1725, and by the “Mar{\'i}a de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0445). J. Villadelprat is supported by the grants MTM2017-86795-C3-2-P and 2017SGR1617. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2022",
doi = "10.1007/s10883-020-09520-3",
language = "Ingl{\'e}s estadounidense",
volume = "28",
pages = "121--150",
}