شماره راهنما :
1178 دكتري
پديد آورنده :
مقيمي، پگاه
عنوان :
انشعابات سيكل هاي حدي در برخي از دستگاه هاي هميلتوني
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، [۱۹۱]ص.: مصور
استاد راهنما :
رسول عاشقي
واژه نامه :
انگليسي به فارسي
توصيفگر ها :
مساله ي شانزدهم هيلبرت , سيكل هاي حدي , انشعاب , دستگاه هميلتوني , تابع ملنيكف , حلقه ي همو كلينيك , حلقه ي هتروكلينيك
استاد داور :
حميدرضا ظهوري زنگنه، حسين خيري استيار، غلامرضا ركني لموكي
تاريخ ورود اطلاعات :
1397/02/31
كد ايرانداك :
ID1178 دكتري
چكيده انگليسي :
Limit Cycle Bifurcation by Perturbing Some Hamiltonian Systems Pegah Moghimi p moghimi@math iut ac ir 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir Advisor Dr Rasool Kazemi r kazemi@kashanu ac ir 2010 MSC 34C07 34C08 37G15 34M50 Keywords Hilbert s 16th problem Limit cycles Bifurcation Hamiltonian system Melnikovfunction Heteroclinic loop Homoclinic loop Abstract This thesis deals with the bifurcations of limit cycles by perturbing some Hamiltonian systems Tostudy the perturbations of Hamiltonian systems the first order Melnikov function plays an importantrole By finding its zeros we can find limit cycles Using he asymptotic expansions of the Melnikovfunction near a Hamiltonian value corresponding to an elementary center a nilpotent center or ahomoclinic or heteroclinic loop with hyperbolic saddles or nilpotent critical points we study the bi furcation problem To study the Poincar bifurcation we may use the Chebysheve criterion developedby Villadelprat The second part of Hilbert s 16th Problem asks about the uniform upper bound H n for themaximum number of limit cycles and their relative positions for the following planar differentialsystem 1 x Pn x y y Qn x y for all possible Pn and Qn where Pn and Qn are real polynomials of degree n in x y However this problem is still open even for the case n 2 but great progress has been made in the theory ofdynamical systems A weaker version of this problem was proposed by Arnold 1 to study the isolatedzeros of Abelian integrals that is called the weak Hilbert s 16th problem More precisely consider a
استاد راهنما :
رسول عاشقي
استاد داور :
حميدرضا ظهوري زنگنه، حسين خيري استيار، غلامرضا ركني لموكي
