dc.contributor.author
Gasull, A.
dc.date.accessioned
2025-01-07T10:40:19Z
dc.date.available
2025-01-07T10:40:19Z
dc.date.issued
2024-09-28
dc.identifier.uri
http://hdl.handle.net/2072/480003
dc.description.abstract
The study of the limit cycles of planar polynomial differential equations is motivated both by its appearance in many mathematical models of the real-world as for the second part of Hilbert's 16th problem. In this work we briefly summarize some results on this subject and we will also highlight the important role that the Abel's differential equations play in its study. In the way, we recall some nice properties of the Riccati's differential equations.
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dc.description.sponsorship
This work is supported by the Spanish State Research Agency, through the projects PID2022-136613NB-I00 grant and the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R &D (CEX2020-001084-M), and grant 2021-SGR-00113 from AGAUR, Generalitat de Catalunya. The author acknowledges all comments and suggestions received from many colleagues and friends that have improved the preliminary versions of this work.Open Access Funding provided by Universitat Autonoma de Barcelona. Open Access Funding provided by Universitat Autonoma de Barcelona.
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dc.format.extent
38 p.
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dc.relation.ispartof
São Paulo Journal of Mathematical Sciences
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dc.rights
(c) 2024 The Author(s)
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dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Polynomial differential equation
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dc.subject.other
Periodic orbit
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dc.subject.other
Limit cycle
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dc.subject.other
Hilbert's 16 h problem
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dc.subject.other
Riccati's equation
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dc.subject.other
Abel's equation
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dc.title
From Abel's differential equations to Hilbert's 16th problem
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1007/s40863-024-00471-2
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
