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Title:
The blow-up method applied to monodromic singularities
Authors:
ID
Ferčec, Brigita
(
Author
)
ID
Giné, Jaume
(
Author
)
Files:
RAZ_Fercec_Brigita_2024.pdf
(501,35 KB)
MD5: 3CB3D10DC36FFB0601305C022A0ED272
https://doi.org/10.14232/ejqtde.2024.1.4
Language:
English
Work type:
Scientific work
Typology:
1.01 - Original Scientific Article
Organization:
FE - Faculty of Energy Technology
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
The blow-up method proves its effectiveness to characterize the integrability of the resonant saddles giving the necessary conditions to have formal integrability and the sufficiency doing the resolution of the associated recurrence differential equation using induction. In this work we apply the blow-up method to monodromic singularities in order to solve the center-focus problem. The case of nondegenerate monodromic singularities is straightforward since any real nondegenerate monodromy singularity can be embedded into a complex system with a resonant saddle. Here we apply the method to nilpotent and degenerate monodromic singularities solving the center problem when the center conditions are algebraic.
Keywords:
monodromic singularity
,
blow-up
,
center problem
,
formal first integral
Publication status:
Published
Publication version:
Version of Record
Submitted for review:
12.06.2023
Publication date:
08.01.2024
Year of publishing:
2024
Number of pages:
18 str.
Numbering:
No. 4
PID:
20.500.12556/DKUM-93732
UDC:
517.5
ISSN on article:
1417-3875
COBISS.SI-ID:
181232643
DOI:
10.14232/ejqtde.2024.1.4
Publication date in DKUM:
25.08.2025
Views:
124
Downloads:
15
Metadata:
Categories:
Misc.
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Record is a part of a journal
Title:
Electronic journal of qualitative theory of differential equations
Shortened title:
Electron. j. qual. theory differ. equ.
Publisher:
Bolyai Institute, University of Szeged
ISSN:
1417-3875
COBISS.SI-ID:
512193561
Document is financed by a project
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
P1-0306-2022
Name:
Uporabna matematika, teoretična fizika in inteligentni sistemi
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-2457-2020
Name:
Fazni prehodi proti koordinaciji v večplastnih omrežjih
Funder:
Other - Other funder or multiple funders
Project number:
PID2020-113758GB-I00
Name:
/
Funder:
Other - Other funder or multiple funders
Project number:
2021SGR0 1618
Name:
/
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:
08.01.2024
Secondary language
Language:
Slovenian
Keywords:
monodromna singularnost
,
razpihovanje
,
problem središča
,
formalni prvi integral
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