Trends in Mathematics Research Perspectives CRM Barcelona Vol.4 Montserrat Corbera Josep Maria Cors Jaume Llibre Andrei Korobeinikov Editors Extended Abstracts Spring 2014 Hamiltonian Systems and Celestial Mechanics Virus Dynamics and Evolution Trends in Mathematics Research Perspectives CRM Barcelona Serieseditors EnricVentura AntoniGuillamon Since1984theCentredeRecercaMatemàtica(CRM)hasbeenorganizingscientific eventssuchasconferencesorworkshopswhichspanawiderangeofcutting-edge topicsinmathematicsandpresentoutstandingnewresults. Inthefallof2012,the CRM decidedto publishextendedconferenceabstractsoriginatingfrom scientific eventshostedatthecenter.Theaimofthisinitiativeistoquicklycommunicatenew achievements,contributeto a fluentupdateofthe state of theart, andenhancethe scientificbenefitoftheCRMmeetings.Theextendedabstractsarepublishedinthe subseriesResearchPerspectivesCRMBarcelonawithintheTrendsinMathematics series.Volumesinthesubserieswillincludeacollectionofrevisedwrittenversions ofthecommunications,groupedbyevents. Moreinformationaboutthisseriesathttp://www.springer.com/series/4961 Extended Abstracts Spring 2014 Hamiltonian Systems and Celestial Mechanics Montserrat Corbera Josep Maria Cors Jaume Llibre Editors Virus Dynamics and Evolution Andrei Korobeinikov Editor Editors MontserratCorbera JosepMariaCors DepartamentdeTecnologiesDigitals, DepartamentdeMatemaJticaAplicadaIII CampusTorredelsFrares UniversitatPoliteJcnicadeCatalunya UniversitatdeVic Manresa,Spain Vic,Spain JaumeLlibre AndreiKorobeinikov DepartamentdeMatemàtiques CentredeRecercaMatemaJtica UniversitatAutònomadeBarcelona Barcelona,Spain Barcelona,Spain ISSN2297-0215 ISSN2297-024X (electronic) TrendsinMathematics ISBN978-3-319-22128-1 ISBN978-3-319-22129-8 (eBook) DOI10.1007/978-3-319-22129-8 LibraryofCongressControlNumber:2015954093 Mathematics Subject Classification (2010): First part: 34C25, 34C29, 65P30, 70H05; Second part: 92D15,92D25,92D30 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.birkhauser-science.com) Contents PartI HamiltonianSystemsandCelestialMechanics OntheForceFieldsWhichAreHomogeneousofDegree(cid:2)3 ............... 3 AlainAlbouy Bifurcations of the Spatial Central Configurations inthe5-BodyProblem........................................................... 9 MarthaÁlvarez-Ramírez,MotserratCorbera,andJaumeLlibre ConvexCentralConfigurationsofTwoTwistedn-gons ..................... 17 EstherBarrabésandJosepMariaCors TheNewtoniann-BodyProblemintheContextofCurvedSpace.......... 23 FlorinDiacu Poincaré Maps and Dynamics in Restricted Planar .nC1/-BodyProblems.......................................................... 27 AntonioGarcía A Methodology for Obtaining Asymptotic Estimates for the Exponentially Small Splitting of Separatrices toWhiskeredToriwithQuadraticFrequencies .............................. 31 AmadeuDelshams,MarinaGonchenko,andPereGutiérrez HomoclinicandHeteroclinicOrbitsforaClassofSingular PlanarNewtonianSystems...................................................... 39 JoannaJanczewska TransportDynamics:FromtheBicirculartotheRealSolar SystemProblem .................................................................. 45 Mercè Ollé, Esther Barrabés, Gerard Gómez, andJosepMariaMondelo v vi Contents Quasi-Periodic Almost-Collision Motions in the Spatial Three-BodyProblem............................................................. 49 JesúsF.Palacián,FloraSayas,andPatriciaYanguas GeneralizedDiscreteNonlinear SchrödingerasaNormal FormattheThermodynamicLimitfortheKlein–GordonChain.......... 53 SimonePaleariandTizianoPenati Stabilityof Euler-Type RelativeEquilibria in the Curved ThreeBodyProblem............................................................. 59 ErnestoPérez-ChavelaandJuanManuelSánchezCerritos Two-DimensionalSymplecticReturnMapsandApplications.............. 65 ReginaMartínezandCarlesSimó CentralConfigurationsofanIsoscelesTrapezoidalFive-Body Problem ........................................................................... 71 Abdulrehman Kashif, Muhammad Shoaib, andAnoopSivasankaran TheDiscreteHamiltonian–HopfBifurcationfor4DSymplecticMaps .... 77 ErnestFontich,CarlesSimó,andArturoVieiro MomentMapoftheActionofSO.3/onR3(cid:3)R3............................. 83 JoséAntonioVillaMorales PartII VirusDynamicsandEvolution Modelling Infection Dynamics and Evolution of Viruses inPlantPopulations.............................................................. 89 AuroraFraileandFernandoGarcía-Arenal TheSpreadofTwoViralStrainsonaPlantLeaf ............................ 95 Juan Carlos Cantero-Guardeño, Vladimir Sobolev, andAndreiKorobeinikov TrackingthePopulationDynamicsofPlantVirusEscapeMutants........ 101 SantiagoF.Elena EvolutionaryEscapeinPopulationswithGenotype-Phenotype Structure.......................................................................... 107 EstherIbáñez-MarceloandTomásAlarcón EvolutionofStalk/SporeRatioinaSocialAmoeba:Cell-to-Cell InteractionviaaSignalingChemicalShapedbyCheatingRisk............ 113 YohIwasa Within-HostViralEvolutionModelwithCross-Immunity ................. 119 NaranivanLaarhovenandAndreiKorobeinikov Contents vii ModellingViralEvolutionandAdaptation ................................... 125 SusannaManrubia ChangesinCodon-PairBiasofHumanImmunodeficiency VirusType1AffectVirusReplication......................................... 131 MiguelÁngelMartínez CompetingNeutralPopulationsofDifferentDiffusivity .................... 137 SimonePigolotti Density-DependentDiffusionandEpidemicsonHeterogeneous Metapopulations ................................................................. 143 AlbertAvinyó,MartaPellicer,JordiRipoll,andJoanSaldaña AreViralBlipsinHIV-1-InfectedPatientsClinicallyRelevant? ........... 149 DanielSánchez-TaltavullandTomásAlarcón ModelsofDevelopmentalPlasticityandCellGrowth ....................... 155 GraemeWake Part I Hamiltonian Systems and Celestial Mechanics Editors MontserratCorbera JosepMariaCors JaumeLlibre Foreword From January to July 2014, the Research Programme Central Configurations, Periodic Orbits and beyond in Celestial Mechanics took place at the Centre de Recerca Matemàtica (CRM), in Bellaterra, Barcelona. It was coordinated by Montserrat Corbera (Universidad de Vic, Spain), Josep Maria Cors (Universitat Politècnica de Catalunya, Spain), and Jaume Llibre (Universitat Autònoma de Barcelona,Spain). Duringtheseintensesevenmonths,severalscientificeventstookplace,including an international conference (the HAMSYS-2014), three advanced courses, and a weekly seminar, all of them with the active participation of many visitors invited toattendfromseveralcountriesabroad.Ofcourse,additionally,allparticipantshad numerousoccasionstohostinformalbutfruitfulconversationsamongthemselves, discussingmathematicalideaswhich,inmanycases,gaverisetonewandinterest- ingresults;altogetherinaverydynamicandproductiveresearchatmosphere. In this volume of the subseries Research Perspectives CRM-Barcelona (pub- lished by Birkhäuser inside the series Trends in Mathematics), we present fifteen Extended Abstracts corresponding to selected talks given by participants in the Research Programme.More than half of them come from talks at the Conference onHamiltonianSystemsandCelestialMechanics2014(HAMSYS2014)(heldfrom June 2nd to 6th, 2014), and the rest come from talks at the weekly seminar held along the first semester of 2014. We hope the presentation of this material under the present Extended Abstract form will give to the authors the opportunity to 2 I HamiltonianSystemsandCelestialMechanics quicklycommunicatetheirrecentresearch:mostoftheshortarticlesherearebrief and preliminarypresentationsof new results not yetpublished in regularresearch journals. We would like to expressourgratitudeto CRM forhostingandsupportingour researchprogramme.AlsoourwarmthankstotheCRMstaff,itsdirector,Joaquim Bruna, and all the secretaries for providing great facilities and a very pleasant workingenvironment.Finally,thanksareduetoallthosewhoattendedthetalks,for theirinterest,theiractiveparticipation,andtheirenthusiasmtowardsmathematics. Vic,Spain MontserratCorbera Manresa,Spain JosepMariaCors Barcelona,Spain JaumeLlibre