95fbd7c06912151b76afa400052a89e0 quathedyn_a2025m4v24n2p70.pdf 38521c3a40e4e40983111868c268ecd19ba56ce2 quathedyn_a2025m4v24n2p70.pdf 6297bdae19f0a5cbe5e461bb722c5d4dd85c771a5be46b4e8705a1a4e083b6df quathedyn_a2025m4v24n2p70.pdf Title: Invariant Graphs and Dynamics of a Family of Continuous Piecewise Linear Planar Maps Subject: Qualitative Theory of Dynamical Systems, https://doi.org/10.1007/s12346-025-01221-1 Keywords: Continuous piecewise linear map; Invariant graph; Markov partition; Periodic orbit; Topological entropy; Rotation number; One-dimensional chaotic dynamics Author: Anna Cima Creator: Springer Producer: Acrobat Distiller 10.1.8 (Windows); modified using iText® 5.3.5 ©2000-2012 1T3XT BVBA (SPRINGER SBM; licensed version) CreationDate: Sat Feb 8 14:39:30 2025 CET ModDate: Tue Feb 11 14:08:51 2025 CET Custom Metadata: yes Metadata Stream: yes Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 103 Encrypted: no Page size: 439.37 x 666.142 pts Page rot: 0 File size: 2899087 bytes Optimized: no PDF version: 1.4 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- RMTDPN+MSBM10 Type 1C WinAnsi yes yes no 98 0 RYYWVH+Times-Italic Type 1C MacRoman yes yes no 99 0 UBTPAY+MSAM10 Type 1C Custom yes yes no 100 0 XBGXIW+MTMI Type 1C Custom yes yes yes 101 0 WYUFYB+MTSYN Type 1C Custom yes yes yes 102 0 MyriadPro-SemiCn Type 1C WinAnsi yes no no 103 0 TEOCDQ+MyriadPro-SemiboldSemiCn Type 1C MacRoman yes yes no 104 0 JLOLJY+MyriadPro-Semibold Type 1C WinAnsi yes yes no 2124 0 FISQRV+MTSYB Type 1C Custom yes yes no 313 0 TYGDAI+MarVoSym Type 1C WinAnsi yes yes no 2125 0 JQMTAD+MyriadPro-Bold Type 1C WinAnsi yes yes no 105 0 JXMOTX+Times-Roman Type 1C Custom yes yes no 106 0 BJAKRQ+Times-Bold Type 1C WinAnsi yes yes no 147 0 MVJUCW+CMSY10 Type 1C WinAnsi yes yes no 208 0 LNATKE+MyriadPro-BoldSemiCn Type 1C WinAnsi yes yes no 249 0 HHHQYD+MTEX Type 1C Custom yes yes yes 254 0 NXRHFE+MyriadPro-SemiboldSemiCnIt Type 1C WinAnsi yes yes no 255 0 POQSPS+MyriadPro-BoldIt Type 1C WinAnsi yes yes no 311 0 TVWCAT+MyriadPro-BoldSemiCnIt Type 1C WinAnsi yes yes no 312 0 RPLSRJ+RMTMIB Type 1C WinAnsi yes yes no 345 0 GACWGB+CMR10 Type 1C WinAnsi yes yes no 346 0 SKMTNH+HVMathBoldItalic Type 1C WinAnsi yes yes no 594 0 SMCUWB+CMSY8 Type 1C WinAnsi yes yes no 716 0 DXHDFB+CMSY7 Type 1C WinAnsi yes yes no 880 0 AAOLOM+CMSY9 Type 1C WinAnsi yes yes no 1024 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-03-22 02:41:33 CET RepresentationInformation: quathedyn_a2025m4v24n2p70.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-03-21 18:06:28 CET Size: 2899087 Format: PDF Version: 1.4 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 2205 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseOutlines Language: EN Outlines: Item: Title: Invariant Graphs and Dynamics of a Family of Continuous Piecewise Linear Planar Maps Destination: Doc-Start Children: Item: Title: Abstract Destination: abscnt.2 Item: Title: 1 Introduction and Main Results Destination: section.1 Item: Title: 2 Preliminary Results Destination: section.2 Children: Item: Title: 2.1 Topological Entropy Destination: subsection.2.1 Item: Title: 2.2 Rotation Numbers and Set of Periods of a Rotation Interval Destination: subsection.2.2 Item: Title: 2.3 Additional Notation Destination: subsection.2.3 Item: Title: 3 The Case age0 Destination: section.3 Children: Item: Title: 3.1 The Case a=1 Destination: subsection.3.1 Item: Title: 3.2 The Case a=0. Proof of Theorem A Destination: subsection.3.2 Item: Title: 4 The Case a<0 (I). Proofs of Theorems B and C Destination: section.4 Children: Item: Title: 4.1 Proof of Theorem B Destination: subsection.4.1 Item: Title: 4.2 Structure of the ω-Limits and Proof of Theorem C Destination: subsection.4.2 Item: Title: 5 The Case a<0 (II). Case Analysis and Proof of Theorem D Destination: section.5 Children: Item: Title: 5.1 The Case a=-1 and bleq-2 Destination: subsection.5.1 Item: Title: 5.2 The Case a=-1 and -2< bleq-1 Destination: subsection.5.2 Item: Title: 5.3 The Case a=-1 and -1< bleq-3/4 Destination: subsection.5.3 Item: Title: 5.4 The Case a=-1 and -3/4 2025-02-08T19:09:30+05:30 Springer 2025-02-11T14:08:51+01:00 2025-02-11T14:08:51+01:00 Acrobat Distiller 10.1.8 (Windows); modified using iText® 5.3.5 ©2000-2012 1T3XT BVBA (SPRINGER SBM; licensed version) Continuous piecewise linear map; Invariant graph; Markov partition; Periodic orbit; Topological entropy; Rotation number; One-dimensional chaotic dynamics application/pdf https://doi.org/10.1007/s12346-025-01221-1 Springer International Publishing Qualitative Theory of Dynamical Systems, https://doi.org/10.1007/s12346-025-01221-1 Continuous piecewise linear map Invariant graph Markov partition Periodic orbit Topological entropy Rotation number One-dimensional chaotic dynamics Invariant Graphs and Dynamics of a Family of Continuous Piecewise Linear Planar Maps Anna Cima Armengol Gasull Víctor Mañosa Francesc Mañosas 10.1007/s12346-025-01221-1 2010-04-23 true springer.com springerlink.com https://doi.org/10.1007/s12346-025-01221-1 10.1007/s12346-025-01221-1 1662-3592 journal Qualitative Theory of Dynamical Systems The Author(s) 2010-04-23 true 10.1007/s12346-025-01221-1 noindex springer.com springerlink.com VoR uuid:ec9529c9-e92a-4186-a638-fd0247fc72dc uuid:25ada051-c5d3-4fa4-a1ce-06311cb0e64c default 1 converted uuid:ec9529c9-e92a-4186-a638-fd0247fc72dc converted to PDF/A-2b pdfToolbox 2025-02-08T19:10:25+05:30 converted uuid:066367f4-5e63-4fbc-886c-850c99249500 converted to PDF/A-2b pdfToolbox 2025-02-08T19:12:23+05:30 2 B http://ns.adobe.com/pdfx/1.3/ pdfx Adobe Document Info PDF eXtension Schema external Mirrors crossmark:MajorVersionDate CrossmarkMajorVersionDate Text external Mirrors crossmark:CrossmarkDomainExclusive CrossmarkDomainExclusive Text internal Mirrors crossmark:DOI doi Text external Mirrors crossmark:CrosMarkDomains CrossMarkDomains seq Text internal A name object indicating whether the document has been modified to include trapping information robots Text internal ID of PDF/X standard GTS_PDFXVersion Text internal Conformance level of PDF/X standard GTS_PDFXConformance Text internal Company creating the PDF Company Text internal Date when document was last modified SourceModified Text http://crossref.org/crossmark/1.0/ crossmark Crossmark Schema internal Usual same as prism:doi DOI Text external The date when a publication was publishe. 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