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韩茂安 著 / 科学出版社 / 2013-02 / 精装
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数学专著系列25 :极限环分支理论(英文)
Thisbookintroducesthebifurcationtheoryoflimitcyclesofplanarsystemswithmultipleparameters.Itisfocusedonthemostrecentdevelopmentsinthisfieldandprovidesmajoradvancesinfundamentaltheoryoflimitcycles.ThemaintopicsincludeHopfbifurcationoflimitcyclesfromacenterorafocus,homoclinicbifurcationsnearahomoclinicoraheteroclinicloop,andthenumberoflimitcyclesinglobalbifurcationsofnear-Hamiltonianpolynomialsystemsofarbitrarydegree.Thisbookwillbeofusetograduatemathematicsstudentsaswellasscientists.
HanMaoanisaprofessorattheInstituteofMathematicalSciencesofShanghaiNormalUniversity.Hehasbeenworkingontheresearchofdifferentialequationsanddynamicalsystemsfor30yearswith300paperspublished.
PrefaceChapter1LimitCycleandItsPerturbations1.1Basicnotationsandfacts1.2Furtherdiscussiononpropertyoflimitcycles1.3PerturbationsofalimitcycleChapter2FocusValuesandHopfBifurcation2.1Poincaremapandfocusvalue2.2NormalformandPoincare-Lyapunovtechnique2.3Hopfbifurcationnearafocusandsystemswithsymmetry2.4DegenerateHopfbifurcationnearacenter2.5HopfbifurcationforLienardsystems2.6HopfbifurcationforsomepolynomialsystemsChapter3PerturbationsofHamiltonianSystems3.1Generaltheory3.2Limitcyclesnearhomoclinicandheteroclinicloops3.3FindingmorelimitcyclesbyMelnikovfunctions3.4Limitcyclebifurcationsnearanilpotentcenter3.5Limitcyclebifurcationswithanilpotentcusp3.6LimitcyclebifurcationswithanilpotentsaddleChapter4StabilityofHomoclinicLoopsandLimitCycleBifurcations4.1Localbehaviornearasaddle4.2Stabilityofahomoclinicloopandbifurcationnearit4.3Homoclinicandheteroclinicbifurcationsinnear-HamiltoniansystemsChapter5TheNumberofLimitCyclesofPolynomialSystems5.1Introduction5.2Somefundamentalresults5.3FurtherstudyforgeneralpolynomialsystemsBibliographyIndex
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