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Title:           The Zero–Hopf bifurcations of the quadratic polynomial differential jerk systems in 
Subject:         Aequationes mathematicae, https://doi.org/10.1007/s00010-025-01182-5
Keywords:        Jeek system; Zero-Hopf bifurcation; Periodic orbits; Averaging theory
Author:          Jaume Llibre 
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      Title: The Zero–Hopf bifurcations of the quadratic polynomial differential jerk systems in mathbbR3
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        Title: Abstract
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        Title: 1. Introduction and statement of the main result
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        Title: 2. Proofs of the results
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        Title: Acknowledgements
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       Item: 
        Title: Appendix: Averaging theory of first order
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        Title: References
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    Keywords: Jeek system; Zero-Hopf bifurcation; Periodic orbits; Averaging theory
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                  <pdfaSchema:schema>Crossmark Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Usual same as prism:doi</pdfaProperty:description>
                           <pdfaProperty:name>DOI</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The date when a publication was publishe.</pdfaProperty:description>
                           <pdfaProperty:name>MajorVersionDate</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>CrossmarkDomainExclusive</pdfaProperty:description>
                           <pdfaProperty:name>CrossmarkDomainExclusive</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>CrossMarkDomains</pdfaProperty:description>
                           <pdfaProperty:name>CrossMarkDomains</pdfaProperty:name>
                           <pdfaProperty:valueType>seq Text</pdfaProperty:valueType>
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               </rdf:li>
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                  <pdfaSchema:namespaceURI>http://prismstandard.org/namespaces/basic/2.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>prism</pdfaSchema:prefix>
                  <pdfaSchema:schema>Prism Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>This element provides the url for an article or unit of content. The attribute platform is optionally allowed for situations in which multiple URLs must be specified. PRISM recommends that a subset of the PCV platform values, namely “mobile” and “web”, be used in conjunction with this element. NOTE: PRISM recommends against the use of the #other value allowed in the PRISM Platform controlled vocabulary. In lieu of using #other please reach out to the PRISM group at prism-wg@yahoogroups.com to request addition of your term to the Platform Controlled Vocabulary.</pdfaProperty:description>
                           <pdfaProperty:name>url</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The Digital Object Identifier for the article.&#xA;The DOI may also be used as the dc:identifier. If used as a dc:identifier, the URI form should be captured, and the bare identifier should also be captured using prism:doi. If an alternate unique identifier is used as the required dc:identifier, then the DOI should be specified as a bare identifier within prism:doi only. If the URL associated with a DOI is to be specified, then prism:url may be used in conjunction with prism:doi in order to provide the service endpoint (i.e. the URL). </pdfaProperty:description>
                           <pdfaProperty:name>doi</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>ISSN for an electronic version of the issue in which the resource occurs. Permits publishers to include a second ISSN, identifying an electronic version of the issue in which the resource occurs (therefore e(lectronic)Issn. If used, prism:eIssn MUST contain the ISSN of the electronic version.</pdfaProperty:description>
                           <pdfaProperty:name>issn</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Volume number</pdfaProperty:description>
                           <pdfaProperty:name>volume</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Issue number</pdfaProperty:description>
                           <pdfaProperty:name>number</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Starting page</pdfaProperty:description>
                           <pdfaProperty:name>startingPage</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Ending page</pdfaProperty:description>
                           <pdfaProperty:name>endingPage</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The aggregation type specifies the unit of aggregation for a content collection. Comment PRISM recommends that the PRISM Aggregation Type Controlled Vocabulary be used to provide values for this element. Note: PRISM recommends against the use of the #other value currently allowed in this controlled vocabulary. In lieu of using #other please reach out to the PRISM group at info@prismstandard.org to request addition of your term to the Aggregation Type Controlled Vocabulary. </pdfaProperty:description>
                           <pdfaProperty:name>aggregationType</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Title of the magazine, or other publication, in which a resource was/will be published. Typically this will be used to provide the name of the magazine an article appeared in as metadata for the article, along with information such as the article title, the publisher, volume, number, and cover date. Note: Publication name can be used to differentiate between a print magazine and the online version if the names are different such as “magazine” and “magazine.com.”</pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Copyright</pdfaProperty:description>
                           <pdfaProperty:name>copyright</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
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                  <pdfaSchema:prefix>pdf</pdfaSchema:prefix>
                  <pdfaSchema:schema>Adobe PDF Schema</pdfaSchema:schema>
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                        <rdf:li rdf:parseType="Resource">
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                           <pdfaProperty:description>A name object indicating whether the document has been modified to include trapping information</pdfaProperty:description>
                           <pdfaProperty:name>Trapped</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:description>UUID based identifier for specific incarnation of a document</pdfaProperty:description>
                           <pdfaProperty:name>InstanceID</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>The common identifier for all versions and renditions of a document.</pdfaProperty:description>
                           <pdfaProperty:name>DocumentID</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>The common identifier for all versions and renditions of a document.</pdfaProperty:description>
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                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>A reference to the original document from which this one is derived. It is a minimal reference; missing components can be assumed to be unchanged. For example, a new version might only need to specify the instance ID and version number of the previous version, or a rendition might only need to specify the instance ID and rendition class of the original.</pdfaProperty:description>
                           <pdfaProperty:name>DerivedFrom</pdfaProperty:name>
                           <pdfaProperty:valueType>ResourceRef</pdfaProperty:valueType>
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                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
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                           <pdfaType:namespaceURI>http://ns.adobe.com/xap/1.0/sType/Part#</pdfaType:namespaceURI>
                           <pdfaType:prefix>stPart</pdfaType:prefix>
                           <pdfaType:type>Part</pdfaType:type>
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                  <pdfaSchema:prefix>pdfaid</pdfaSchema:prefix>
                  <pdfaSchema:schema>PDF/A ID Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Part of PDF/A standard</pdfaProperty:description>
                           <pdfaProperty:name>part</pdfaProperty:name>
                           <pdfaProperty:valueType>Integer</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Amendment of PDF/A standard</pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Conformance level of PDF/A standard</pdfaProperty:description>
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                  <pdfaSchema:prefix>xmpTPg</pdfaSchema:prefix>
                  <pdfaSchema:schema>XMP Paged-Text</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>XMP08 Spec: An ordered array of plate names that are needed to print the document (including any in contained documents).</pdfaProperty:description>
                           <pdfaProperty:name>PlateNames</pdfaProperty:name>
                           <pdfaProperty:valueType>Seq Text</pdfaProperty:valueType>
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                  <pdfaSchema:prefix>jav</pdfaSchema:prefix>
                  <pdfaSchema:schema>NISO</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Values for Journal Article Version are one of the following:&#xA;AO = Author’s Original&#xA;SMUR = Submitted Manuscript Under Review&#xA;AM = Accepted Manuscript&#xA;P = Proof&#xA;VoR = Version of Record&#xA;CVoR = Corrected Version of Record&#xA;EVoR = Enhanced Version of Record</pdfaProperty:description>
                           <pdfaProperty:name>journal_article_version</pdfaProperty:name>
                           <pdfaProperty:valueType>Closed Choice of Text</pdfaProperty:valueType>
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                  </pdfaSchema:property>
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       AppearanceDictionary: true
       Destination: 100
      Annotation: 
       Subtype: Link
       Rect: 370, 383, 382, 391
       Flags: Print
       AppearanceDictionary: true
       Destination: 100
     Thumb: true
    Page: 
     Label: 12
     Thumb: true
    Page: 
     Label: 13
     Thumb: true
  Checksum: 698c64da
   Type: CRC32
  Checksum: 628050350fdbbc6e5707c413f6cc549f
   Type: MD5
  Checksum: d3847c94d2aecb192310d7a3b28080931eae0444
   Type: SHA-1
  Checksum: 2939800990504730b0fcfa504ab84d96fe1687727a7c9fd52a4bbc0eadeacdf6
   Type: SHA-256