پديد آورنده :
گودرزي، حميدرضا
عنوان :
تعداد سيكل هاي حدي در اختلالات كوچك رده اي از دستگاه هاي هليتوني فوق بيضوي با يك زين پوچ توان
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هشت،99ص.: مصور
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رسول عاشقي
استاد مشاور :
حميدرضا ظهوري زنگنه
توصيفگر ها :
سيكل مهري , سيستم هاي هميلتوني , انتگرال آبلي , اختلال
تاريخ نمايه سازي :
23/11/91
استاد داور :
محمدرضا رئوفي، رضا مزروعي
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
On The Number Of Limit Cycles In Small Perturbations Of A Class Of Hyper Elliptic Hamiltonian Systems With One Nilpotent Saddle HamidReza Goodarzi hr gudarzi@gmail com 12 09 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi rasoul asheghi@cc iut ac ir Advisor Dr HamidRezaZohouriZangeneh hamidz@cc iut ac ir 2010 MSC 34C05 34C23 58F05 Keywords Hyper elliptic Hamiltonian systems Nilpoten tsaddle Abelian integrals Limit cycles AbstractThis thesis is an extension and modi ation of the work done by Jihua Wang and Dongmei Xiao 15 In this thesis we make a complete study on small perturbations of a Hamiltonian vector eld witha hyper elliptic Hamiltonian of degree ve which is a Lienard system of the form x y y Q1 x yQ2 x with Q1 x x x 1 3 and Q2 x a b x c x2 x3 where 0 1 a b and c are real bounded parameters This system has two critical points O 0 0 and E 1 0 where undergo perturbation does not change the number and position of equilibria For each value ofparameters a b c equilibria O 0 0 and E 1 0 are kept and E 1 0 always is a degenerated saddlewith one zero eigenvalue or two zero eigenvalues for 0 1 If parameters a b c are in a smallneighborhood of 0 14 15 then this system has at most three limit cycles in the plane for 0 1 5 14More exactly for any given with 0 1 a series Hopf bifurcations occur near equilibrium O 0 0 of this system in a small neighborhood of bifurcation value a b c 0 14 15 In particular a 5 14unique unstable limit cycle bifurcates from equilibrium O 0 0 of this system as a 0 c 3b and 5b increases from 14 a unique stable limit cycle bifurcates from equilibrium O 0 0 of this system as 5 14b 5 14 and c 3b increases from 0 and a unique unstable limit cyclea 0 b 0 c 3b 20 c 3b 0 c 3b a 0 and parameter 5bifurcates from equilibrium O 0 0 of this system as b 14 6
استاد راهنما :
رسول عاشقي
استاد مشاور :
حميدرضا ظهوري زنگنه
استاد داور :
محمدرضا رئوفي، رضا مزروعي
