Bifurcations of Zeros in Translated Families of Functions and Applications

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 an...

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Bibliographic Details
Published in:Journal of dynamical and control systems 2022, Vol.28 (1), p.121-150
Main Authors: Mardešić, P., Marín, D., Villadelprat, J.
Format: Article
Language:English
Subjects:
Bifurcations
Calculus of Variations and Optimal Control
Optimization
Control
Dynamical Systems
Dynamical Systems and Ergodic Theory
Engineering Sciences
Mathematics
Mathematics and Statistics
Systems Theory
Vibration
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Summary: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.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-020-09520-3