پديد آورنده :
مقيمي، پگاه
عنوان :
مسئله ي شانزدهم هيلبرت براي معادلات لينارد كلاسيك از درجه ي زوج
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي﴿ دستگاه هاي ديناميكي﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
[هشت] ، 113ص: مصور
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
حميد رضا ظهوري زنگنه
توصيفگر ها :
سيكل حدي , اتصال هترو كلينيك , سيكل پذيري
تاريخ نمايه سازي :
19/11/88
استاد داور :
فريد بهرامي، رسول عاشقي
چكيده فارسي :
به فارسي و انگليسي:قابل رويت در نسخه ديجيتال
چكيده انگليسي :
Hilbert s 16th Problem for Classical Li nard Equations of Even e Degree Pegah Moghimi p moghimi@math iut ac ir October 26 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir2000 MSC 34C07 34C37 34D10 Key words Classical Li nard equation Limit cycle Heteroclinic connection Cyclicity e Abstract In this thesis we present an expanded account of Hilbert s 16th problem for classicalLi nard equations of even degree based on article by M Caubergh and F Dumortier 2007 eHilbert s 16th problem asks for the maximum number of limit cycles that a polynomial vector eld for a given degree in the plane can have Although the problem is more than 100 yearsold it is not even known whether a uniform upper bound only depending on the degree of thevector eld might exist even not when the degree is two In the year 2000 S Smale addedthe question to his list of problems for the 21st century but restricting it to the classicalLi nard equations eClassical Li nard equations are two dimensional vector elds on the phase plane or on the eLi nard plane related to scaler di erential equations x f x x x 0 In this thesis we e consider f to be a polynomial of degree 2l 1 with l a xed but arbitrary natural number The related Li nard equation is of degree 2l eThe best that one seems able to do in case n 2l 1 whit l 1 is to compactify the planeto the appropriate Poincare Lyapunov disc By this compacti cation there is a possibilityof encountering a heterclinic connection between two semi hyperbolic saddles at in nity Together with part of the circle at in nity this gives rise to a non hyperbolic two saddlecycle From it large amplitude limit cycles can be perturbed In this thesis we make acomplete study of these limit cycles providing precise cyclicity results for these two saddlecycles Let P2l 1 R denote set of polynomials f x of degree at most 2l 1 on which weconsider as usual the coe cient topology and BR 0 denote the ball around origin havingradius R The main result of this thesis is the following Theorem 1 Main Theorem let K P2l 1 R be compact and consisting of polynomialsof degree exactly 2l 1 then there exists R 0 such that any system X having an Li nard e 2equation with f K has at most l limit cycles having intersection with R BR 0 We call such limit cycles having an intersection with R2 BR 0 large amplitude limit cycles 1
استاد راهنما :
حميد رضا ظهوري زنگنه
استاد داور :
فريد بهرامي، رسول عاشقي
