پديد آورنده :
سلطاني، شبنم
عنوان :
سيكل هاي حدي ميدان هاي برداري خطي روي منيفلدها
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، [۱۰۳]ص.: مصور
استاد راهنما :
رسول عاشقي
استاد مشاور :
اعظم اعتماد
واژه نامه :
انگليسي به فارسي; فارسي به انگليسي
توصيفگر ها :
سيكل حدي , مدار تناوبي , مركز , مركز هم دوره , روش معدل گيري
استاد داور :
حميدرضا ظهوري زنگنه، رسول كاظمي
تاريخ ورود اطلاعات :
1396/11/03
چكيده انگليسي :
Limit Cycles Of Linear Vector Fields On Manifolds Shabnam Soltani shabnam soltani@math iut ac ir 13 12 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 34C05 92C80 Keywords limit cycle periodic orbit center isochoronous center averaging method Abstract It is well known that linear vector elds on the manifold Rn cannot have limit cycles but thisis not the case for linear vector elds on other manifolds We study the periodic orbits of linearvector elds on di erent manifolds and motivate and present an open problem on the number oflimit cycles of linear vector elds on a class of C 1 connected manifolds In qualitative theory theperiodic orbits play an important role in the study of the dynamics of ordinary di erential equationsor vector elds Inside the periodic orbits there is a class of limit cycles a limit cycle is a periodicorbit isolated in the set of all the periodic orbits of the di erential equation or vector eld Manypieces of work have been done on the limit cycles of many di erent di erential equations see forinstance 9 12 15 18 23 27 and the references quoted therein but as far as we know nobody has paidany attention to the limit cycles of linear vector elds probably because the vector elds on Rn haveno limit cycles But there are some interesting questions regarding the linear vector elds on othermanifolds Demonstrating some of these questions is the objective of this thesis Linear vector eldsare the easiest of the vector elds but they play an important role in the theory of di erential systemsand also in applications We deal with C 1 connected manifolds and the C 1 vector elds on them IfM is a C 1 connected manifold and T M is its tangent bundle here a vector eld X on M is a C 1 mapX M T M such that X x Tx M where Tx M is the tangent space to M at the point x Alinear vector eld on Rn is a vector eld X de ned as X x Ax b where x b Rn and A is a realn n matrix Since the solutions of a linear vector eld on Rn are well known see for instance 2 it follows that when one of these vector elds has a periodic orbit it is not isolated in the set of all
استاد راهنما :
رسول عاشقي
استاد مشاور :
اعظم اعتماد
استاد داور :
حميدرضا ظهوري زنگنه، رسول كاظمي
