8480

7861

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

نه،113ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

حميدرضا ظهوري زنگنه

مجيد گارز

8/11/92

رسول عاشقي، رضا مزروعي سبداني

رياضي

ID7861

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

The cyclicity of period annuli of a class of quadratic reversible systems Mohsen Zarei mohsen zarei1@math iut ac ir 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir Advisor Dr Majid Gazor mgazor@cc iut ac ir 2010 MSC 05C15 53C42 Keywords Limit cycles Abelian integral Quadratic reversible centers AbstractThis thesis deals with the number of limit cycles for small quadratic perturbations of quadraticintegrable systems x Hy x y f x y M x y 1 5 y Hx x y g x y M x y Where is a small parameter and f x y g x y are quadratic polynomials in x y with coe cientsdepending analytically on H x y is the rst integral of the unperturbed system 1 5 0 with theintegrating factor M x y The plane quadratic systems with at least one center are always integrable which can be classi edinto the following four classes Hamiltonian QH reversible QR codimension four Q4 and generalized 3 3Lotka Volterra QLV A natural problem is asking for a maximal number of limit cycles bifurcated 3from the period annulus of these four classes of systems under small quadratic perturbations For theHamiltonian QH this number is closely related to the weak Hilbert 16th problem in the quadratic 3case It is well known that the weak Hilbert 16th problem for Hamiltonian QH was solved completely 3by many authors see 4 13 and the references therein The next natural step is to nd the upperbound of the number of limit cycles which bifurcated from the period annulus of quadratic integrablebut non Hamiltonian systems under quadratic perturbation As usual we use the notion of cyclicity

حميدرضا ظهوري زنگنه

مجيد گارز

رسول عاشقي، رضا مزروعي سبداني