پديد آورنده :
نصر اصفهاني، فاطمه
عنوان :
فرم هاي نرمال و انتگرال هاي اول موضعي معادلات ديفرانسيل غير خطي خود گردان
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هشت، [63]ص.: مصور
يادداشت :
ص.ع. به فارسي و انگليسي
استاد مشاور :
حميدرضا ظهوري زنگنه
توصيفگر ها :
فرم نرمالپوانكاره - دولاك , تشديد , سيستم هاي منفرد
تاريخ نمايه سازي :
30/2/94
استاد داور :
محمدرضا رئوفي، رضا مزروعي سبداني
تاريخ ورود اطلاعات :
1396/09/27
چكيده انگليسي :
واژهنامه انگل سي به فارسي ۶۴Normal forms and local rst integral for nonlinear autonomous di erential equations Fateme Nasr Isfahani fateme nasr@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Majid Gazor mgazor@cc iut ac ir Advisor Dr Hamidreza Zohouri Zangeneh hamidz@cc iut ac ir 2010 MSC 37B15 34A34 37A25 94A60 39A33 37D45 Keywords First integral Poincare Dulac normal form Resonant Singular system AbstractThe question whether a di erential equation admits nonconstant rst integrals in the neighborhood ofa stationary point is of considerable interest for its qualitative analysis On the other hand to detectthe existence of a local rst integral is frequently a di cult problem In the present paper we discussdi erential systems with analytic right hand side and approach the problem via Poincar Dulacnormal forms Thus we will obtain a clear picture of formal rst integrals and some nontrivial resultsabout local analytic rst integrals Let U be an open neighborhood of 0 in Cn and let f U Cnbe an analytic vector valued function with f 0 0 In this work we discuss autonomous di erentialsystems of the form x f x f1 x fn x x x1 xn Since real analytic systems may be extended to Cn our results will also be applicable to the realsetting To f there corresponds a vector eld i e a derivation of local analytic functions given by n f fi 0 xi i 0We will employ di erential equation and vector eld interpretations simultaneously To the commu tator of two derivations there corresponds the Lie bracket of vector valued functions If is a localanalytic function then we call f the Lie derivative of If f 0 then we call a rst integralof the di erential equation Note that we include constant functions in this de nition In this thesiswe investiage dimansion of rst integral s algebra and the form of formal analytic rst integralsfor local autonomous di erential equation near a stationary point We rst decompose the jacobianmatrix near xed point into semi simple and nilpotent part i e A As An and we nd the rstintegrals of semi simple part Now we can get number and form of local rst integrals for system Oneof the usefull implements for this purpose is the Poincare Dulac normal forms The existence questionfor formal rst integrals the ralation of normal forms and rst integrals and convergence of normalforms by various examples for realization of matters will be discussed in that in chapter 3 We willproceed in chapter 4 to characterize and discuss the maximal scenario when all rst integrals of As areconserved by the system transformed to normal form Then we present a class of generalized reversiblesystems that conserve all rst integrals of the linear part and we discuss the case when some of theeigenvalues are zero in the linearization with no other resonances and we generalize known theoremsrelating local manifolds of stationary points to the existence of analytic rst integrals In chapter 5 bysl 2 represention theory we express application of normal forms in rst integral computing for Hopf Takens Bogdanov and Hopf zero singularities
استاد مشاور :
حميدرضا ظهوري زنگنه
استاد داور :
محمدرضا رئوفي، رضا مزروعي سبداني
