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ON THE CROSSING LIMIT CYCLES CREATED BY A DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEM FORMED BY THREE LINEAR HAMILTONIAN SADDLES

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dc.creatorMARIA ELISA ANACLETO HOYOS
dc.creatorJOSÉ CLAUDIO VIDAL DÍAZ
dc.date2024
dc.date.accessioned2025-01-10T15:52:09Z
dc.date.available2025-01-10T15:52:09Z
dc.date.issued2024
dc.description.abstractWE STUDY PLANAR DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS FORMED BY THREE LINEAR HAMILTONIAN SADDLES SEPARATED BY THE NON-REGULAR LINE $ \SIGMA =\{(X,Y)\IN \MATHBB {R}2: (Y=0) \VEE (X=0 \WEDGE Y\GEQ 0)\} $ SIGMA={(X,Y)IS AN ELEMENT OF R2:(Y=0)BOOLEAN OR(X=0 BOOLEAN AND Y >= 0)}. WE PROVE THAT WHEN THE LINEAR HAMILTONIAN SADDLES ARE HOMOGENEOUS THEY HAVE NO LIMIT CYCLES, AND WHEN THEY ARE NON HOMOGENEOUS THEY CAN HAVE AT MOST THREE LIMIT CYCLES HAVING EXACTLY ONE POINT ON EACH BRANCH OF SIGMA, AND AT MOST ONE LIMIT CYCLE HAVING FOUR INTERSECTION POINTS ON SIGMA. MOREOVER WE SHOW THAT THEY CAN HAVE AT MOST ONE LIMIT CYCLE HAVING FOUR INTERSECTION POINTS ON SIGMA AND THREE LIMIT CYCLES HAVING THREE INTERSECTION POINTS ON SIGMA, SIMULTANEOUSLY. THUS WE HAVE SOLVED THE EXTENSION OF THE 16TH HILBERT PROBLEM TO THIS CLASS OF PIECEWISE DIFFERENTIAL SYSTEMS. FURTHERMORE WE SHOW THAT FOR THE THREE TYPES OF COMBINATIONS OF THE LIMIT CYCLES HERE STUDIED IN TWO OF THEM THE UPPER BOUND IS SHARP BY PROVIDING EXAMPLES OF THESE SYSTEMS WITH THE MAXIMUM NUMBER OF POSSIBLE LIMIT CYCLES. FOR THE REMAINING TYPE OF LIMIT CYCLES THE UPPER BOUND IS FOUR AND WE HAVE EXAMPLES WITH THREE LIMIT CYCLES. SO AT THIS MOMENT IT IS AN OPEN PROBLEM TO KNOW IF THE SHARP UPPER BOUND IS EITHER FOUR OR THREE.
dc.formatapplication/pdf
dc.identifier.doi10.1080/14689367.2024.2391417
dc.identifier.issn1468-9375
dc.identifier.issn1468-9367
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/14030
dc.languagespa
dc.publisherDYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL
dc.relation.uri10.1080/14689367.2024.2391417
dc.rightsPUBLICADA
dc.subjectlinear Hamiltonian saddles
dc.subjectLimit cycles
dc.subjectfirst integrals
dc.subjectdiscontinuous piecewise differential systems
dc.titleON THE CROSSING LIMIT CYCLES CREATED BY A DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEM FORMED BY THREE LINEAR HAMILTONIAN SADDLES
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
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