Extended Abstracts Spring 2014: Hamiltonian Systems and Celestial Mechanics; Virus Dynamics and Evolution

150 Pages·2014·3.046 MB·English

by  Montserrat Corbera (ed.), Josep Maria Cors (ed.), Jaume Libre (ed.), Andrei Korobeinikov (ed.)

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.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.
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