شماره راهنما :
1206 دكتري
پديد آورنده :
مختاري، فهيمه
عنوان :
فرم نرمال برخي از ميدان هاي برداري منفرد سه بعدي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
يازده، [۹۵]ص.: مصور
استاد مشاور :
محمدرضا رئوفي
واژه نامه :
انگليسي به فارسي; فارسي به انگليسي
توصيفگر ها :
جبرپواسون , فرمول هاي تكنيكي , خواص هندسي , فرم نرمال مداري
استاد داور :
رضا خوش سيرقاضياني، مليحه يوسف زاده، رسول عاشقي
تاريخ ورود اطلاعات :
1397/04/12
كد ايرانداك :
ID1206 دكتري
چكيده انگليسي :
Normal Forms of Some Three Dimensional Singular Vector Fields Fahimeh Mokhtari f mokhtari@math iut ac ir June 17 2018 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Majid Gazor mgazor@cc iut ac ir Advisor Dr Mohammad Reza Raoo raoo @cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran AbstractIn this thesis we study normal forms of some three dimensional singularities In this directionwe introduce a sl2 invariant family of nonlinear vector elds with a non semisimple triple zerosingularity Indeed we are concerned with characterization and normal form classi cation ofthese vector elds We show that the family constitutes a Lie algebra structure and eachvector eld from this family is solenoidal completely integrable and rotational All suchvector elds share a common quadratic invariant We provide a Poisson structure for theLie algebra from which the second invariant for each vector eld can be readily derived Weshow that each vector eld from this family can be uniquely characterized by two alternativerepresentations one uses a vector potential while the other uses two functionally independentClebsch potentials Our normal form results are designed to preserve these structures andrepresentations The results are implemented in Maple in order to compute vector potentialand the Clebsch potential normal forms of a given vector eld from this family Some practicalnormal form coe cient formulas for degrees of up to four are presented Furthermore weconsider the simplest normal form computation x 2xf x y 2 z 2 y z yf x y 2 z 2 z y zf x y 2 z 2 where f is a formal function with real coe cients and without any constant term These arethe classical normal forms of a larger family of systems with Hopf Zero singularity Indeed these are de ned such that this family would be a Lie subalgebra for the space of all classicalnormal form vector elds with Hopf Zero singularity The simplest normal forms and simplestorbital normal forms of this family with nonzero quadratic part are computed We also obtainthe simplest parametric normal form of any non degenerate perturbation of this family withinthe Lie subalgebra The symmetry group of the simplest normal forms is also discussed Thisis a part of our results in decomposing the normal forms of Hopf Zero singular systems intosystems with a rst integral and nonconservative systems 1
استاد مشاور :
محمدرضا رئوفي
استاد داور :
رضا خوش سيرقاضياني، مليحه يوسف زاده، رسول عاشقي
