Nonlinear Maps and their Applications: Selected Contributions from the NOMA 2013 International Workshop PDF
Preview Nonlinear Maps and their Applications: Selected Contributions from the NOMA 2013 International Workshop
SpringerProceedingsinMathematics&Statistics Volume 112 SpringerProceedingsinMathematics&Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, in- cluding OR and optimization. In addition to an overall evaluation of the interest, scientificquality,andtimelinessofeachproposalatthehandsofthepublisher,indi- vidualcontributionsareallrefereedtothehighqualitystandardsofleadingjournals inthefield.Thus,thisseriesprovidestheresearchcommunitywithwell-edited,au- thoritativereportsondevelopmentsinthemostexcitingareasofmathematicaland statisticalresearchtoday. Moreinformationaboutthisseriesathttp://www.springer.com/series/10533 Ricardo López-Ruiz • Danièle Fournier-Prunaret Yoshifumi Nishio • Clara Grácio Editors Nonlinear Maps and their Applications Selected Contributions from the NOMA 2013 International Workshop 2123 Editors RicardoLópez-Ruiz DanièleFournier-Prunaret FacultaddeCiencias UniversitédeToulouse,LAAS-CNRS,INSA UniversidaddeZaragoza Toulouse Zaragoza France Spain YoshifumiNishio ClaraGrácio DepartmentofE.E.Eng. DepartmentofMathematics TokushimaUniversity UniversityofÉvora,CIMA-UE Tokushima Évora Japan Portugal ISSN2194-1009 ISSN2194-1017(electronic) SpringerProceedingsinMathematics&Statistics ISBN978-3-319-12327-1 ISBN978-3-319-12328-8(eBook) DOI10.1007/978-3-319-12328-8 MathematicsSubjectClassification(2010):39-06,37-06,37E05,37E30,46T20 LibraryofCongressControlNumber:2015934824 SpringerChamHeidelbergNewYorkDordrechtLondon © SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsorthe editorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforanyerrors oromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface ThechaptersinthisvolumeoftheSpringerProceedingsinMathematics&Statis- tics series, entitled Nonlinear Maps andTheirApplications, come from the works presentedintheFourthInternationalWorkshoponNonlinearMapsandTheirAppli- cations(NOMA2013),whichtookplaceinZaragoza,Spain,3–4September,2013. TheworkshopwaslocallyorganizedbyRicardoLópez-Ruiz(RLR)andhostedby theUniversityofZaragozaatitsFacultyofSciences. ThisconferencefollowsthesequenceofWorkshoponNonlinearMapsandTheir ApplicationswhichstartedinToulouse2007,andcontinuedinUrbino2009andin Évora2011. TheobjectiveoftheNOMA2013Conferencewastoprovideaforuminthefield of discrete dynamical systems. It was open for theoretical studies as well as for applications.Theinteractionandtheknowledgeexchangeamongmathematicians, physicists, engineers, andotherspecialists, andyoungresearchers, fromnonlinear scienceswasveryfruitfulandgaverisetonewinsightsinthisarea,inthepleasant atmosphereprovidedbythetownofZaragoza. Itconsistedoffiveinvitedlectures given byYves Pomeau (École Normale Supérieure de Paris, France), Oreste Piro (University of Balearic Islands, Spain), Víctor Man˜osa (Polytechnic University of Catalunya,Spain),ElenaBlokhina(UniversityCollegeDublin,Ireland),andAnir- ban Chakraborti (École Centrale de Paris, France) as well as over 20 contributed lecturesof15differentcountries(Portugal,Japan,France,Spain,CzechRepublic, Russia, Belgium, Iran, Poland, Mexico,Venezuela, Brazil, Tunisia, Germany, and Argentina). Thisvolumeisacompilationoftheselectedworkspresentedintheworkshopand thathavebeenacceptedforpublication.Thediversifiednatureoftheconferenceis reflectedinthespectrumofthe17chapterspublishedhere,where36researchersare contributing. Theeditors,speciallythelocalorganizer(RLR),wouldliketothankallconference participants, committees, authors, who submitted papers for this volume, for their valuablecontribution,aswellasreviewersfortheirtimeandexpertisetoreviewthe workspresentedhere. Editors:RicardoLópez-Ruiz,DanièleFournier-Prunaret,YoshifumiNishio,Clara Grácio. v Contents 1 StudyofAModelfortheDistributionofWealth .................. 1 YvesPomeauandRicardoLópez-Ruiz 2 PeriodicOrbitsofPlanarIntegrableBirationalMaps ............. 13 ImmaGálvez-CarrilloandVíctorMañosa 3 Discrete-TimeModellingofSigma-DeltaInspiredSystemsforMEMS 37 E.Blokhina,P.Giounanlis,M.Dominguez-Pumar,S.Gorreta, J.Pons-NinandO.Feely 4 KineticExchangeModelsinEconomicsandSociology............. 69 SanchariGoswamiandAnirbanChakraborti 5 NonlinearMaps:FromtheToulouseColloqium(1973)toNOMA’13 89 ChristianMira 6 LebesgueMeasureofRecurrentScrambledSets.................. 115 MarekLampart 7 OntheConceptofIntegrabilityforDiscreteDynamicalSystems. InvestigationofWanderingPointsofSomeTraceMap. ............ 127 S.S.Bel’mesovaandL.S.Efremova 8 DiscreteMapsandtheProblemofRoundTripTimeScaleNonlinear DynamicsinSolid-StateLasers ................................. 159 M.V.Gorbunkov,Yu.Ya.Maslova,V.A.Petukhov,M.A.Semenov andYu.V.Shabalin 9 TheImportanceoftheStrategyinBackwardOrbits .............. 171 CarmenPellicer-LostaoandRicardoLópez-Ruiz 10 MinimalCantorTypeSetsonDiscreteDynamicalSystems......... 183 FranciscoBalibrea vii viii Contents 11 PiecewiseExpandingMapsandConjugacyEquations............. 193 CristinaSerpaandJorgeBuescu 12 InSearchofH-theoremforUlam’sRedistributionofEnergyProblem 203 SergeyM.Apenko 13 RandomMarketModelswithanH-Theorem .................... 215 R.López-Ruiz,E.ShivanianandJ.L.López 14 SynchronizationandPhaseOrderinginGloballyCoupledChaotic Maps ........................................................ 227 O.Alvarez-LlamozaandM.G.Cosenza 15 MaximizingaPsychologicalUpliftinLoveDynamics.............. 241 MalayBanerjee,AnirbanChakrabortiandJun-ichiInoue 16 FromWeakAlleeEffecttoNoAlleeEffectinRichards’Growth Models....................................................... 253 J.LeonelRocha,Abdel-KaddousTahaandD.Fournier-Prunaret 17 SystolesonCompactRiemannSurfaceswithSymbolicDynamics... 269 ClaraGrácio Contributors OAlvarez-Llamoza DepartamentodeFísica, FACYT,UniversidaddeCarabobo, Valencia,Venezuela SergeyM.Apenko PNLebedevPhysicalInstitute,Moscow,Russia FranciscoBalibrea DepartamentodeMatemáticas,UniversidaddeMurcia,Mur- cia,Spain Malay Banerjee Department of Mathematics and Statistics, Indian Institute of Technology,Kanpur,India S. S. Bel’mesova N.I.Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod,Russia E. Blokhina School of Electrical, Electronic and Communications Engineering, UniversityCollegeDublin,Dublin,Ireland JorgeBuescu CentrodeMatemáticaeAplicaçõesFundamentais,Departamentode Matemática,FaculdadedeCiências,UniversidadedeLisboa,Lisboa,Portugal Anirban Chakraborti School of Computational and Integrative Sciences, Jawa- harlalNehruUniversity,NewDelhi,India M.G.Cosenza CentrodeFísicaFundamental,UniversidaddeLosAndes,Mérida, Venezuela M. Dominguez-Pumar Universitat Politécnica de Catalunya, Micro- and Nan- otechnologyGroup,Barcelona,Spain L. S. Efremova N. I. Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod,Russia O. Feely School of Electrical, Electronic and Communications Engineering, UniversityCollegeDublin,Dublin,Ireland Danièle Fournier-Prunaret LAAS-CNRS, INSA, University of Toulouse, Toulouse,France ix x Contributors Imma Gálvez-Carrillo Departament de Matemàtica Aplicada III, Universitat PolitècnicadeCatalunya,Barcelona,Spain P.Giounanlis SchoolofElectrical, ElectronicandCommunicationsEngineering, UniversityCollegeDublin,Dublin,Ireland M.V.Gorbunkov P.N.LebedevPhysicsInstitute,Moscow,Russia S. Gorreta Universitat Politécnica de Catalunya, Micro- and Nanotechnology Group,Barcelona,Spain SanchariGoswami S.N.BoseNationalCentreforBasicSciences,Kolkata,India ClaraGrácio CIMA-UE-DMAT,SchoolofScienceandTechnology,Universityof Évora,Évora,Portugal Jun-ichiInoue GraduateSchoolofInformationScienceandTechnology,Hokkaido University,Sapporo,Japan JoséLuisLópez Dept.ofMath.EngineeringandInformatics,PublicUniversityof Navarre,Pamplona,Spain Ricardo López-Ruiz Department of Computer Science & BIFI, University of Zaragoza,Zaragoza,Spain Marek Lampart Department of Applied Mathematics & IT4Innovations, VŠB- TechnicalUniversityofOstrava,Ostrava,CzechRepublic Víctor Mañosa Departament de MatemàticaAplicada III, Universitat Politècnica deCatalunya,Barcelona,Spain Yu.Ya.Maslova P.N.LebedevPhysicsInstitute,Moscow,Russia ChristianMira Quint,Fance CarmenPellicer-Lostao BIFI,UniversityofZaragoza,Zaragoza,Spain V.A.Petukhov P.N.LebedevPhysicsInstitute,Moscow,Russia YvesPomeau DepartmentofMathematics,UniversityofArizona,Tucson,USA J. Pons-Nin Universitat Politécnica de Catalunya, Micro- and Nanotechnology Group,Barcelona,Spain J. Leonel Rocha Instituto Superior de Engenharia de Lisboa - ISEL, ADM and CEAUL,Lisboa,Portugal M.A.Semenov P.N.LebedevPhysicsInstitute,Moscow,Russia CristinaSerpa CentrodeMatemáticaeAplicaçõesFundamentais,Departamento deMatemática,FaculdadedeCiências,UniversidadedeLisboa,Lisboa,Portugal
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