dc.contributor.author
De Maesschalck, P.
dc.contributor.author
Torregrosa, J.
dc.date.accessioned
2025-06-16T10:14:48Z
dc.date.available
2025-06-16T10:14:48Z
dc.date.issued
2025-07-15
dc.identifier.uri
http://hdl.handle.net/2072/484447
dc.description.abstract
By considering planar slow-fast systems with a curve of double singular points, we obtain lower bounds on the number of limit cycles of polynomial systems surrounding a single singular point, as well as on the number of critical periods in one annulus of periodic orbits. In some circumstances, orbits of such slow-fast systems do not exhibit the typical slow-fast behavior but instead follow a hit-and-run pattern: they quickly move toward the critical curve, pause briefly there, and then continue their path.
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dc.description.sponsorship
This work has been funded by Flanders FWO agency (G0F1822N grant); the Catalonia AGAUR agency (2021 SGR 00113 grant); the Spanish Ministerio de Ciencia, Innovaci\u00F3n y Universidades - Agencia Estatal de Investigaci\u00F3n (PID2022-136613NB-I00 grant), the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R& (CEX2020-001084-M grant). ; Funding text 2: This work has been funded by Flanders FWO agency (G0F1822N grant); the Catalonia AGAUR agency (2021 SGR 00113 grant); the Spanish Ministerio de Ciencia, Innovaci\u00F3n y Universidades - Agencia Estatal de Investigaci\u00F3n (PID2022-136613NB-I00 grant), the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R& (CEX2020-001084-M grant). We would like to thank the kind hospitality of the research team of Universitat de les Illes Balears who gave us the opportunity to work together for this work. This project was mainly carried out during a research visit of both authors to UIB. We thank the anonymous referees for their careful review of our initial version. Their comments have helped improve the clarity of the manuscript.
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dc.format.extent
24 p.
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dc.relation.ispartof
Journal of Differential Equations
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dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Critical periods
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dc.subject.other
Non-hyperbolic slow-fast systems
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dc.title
Limit cycles and critical periods with non-hyperbolic slow-fast systems
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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
10.1016/j.jde.2025.113307
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
