پديد آورنده :
بكراني، ناهيد
عنوان :
روش هاي معدل گيري از مرتبه ي دلخواه، جواب هاي تناوبي و انتگرال پذيري
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه، [۱۰۷]ص.: مصور
استاد راهنما :
رسول عاشقي
واژه نامه :
انگليسي به فارسي
توصيفگر ها :
سيستم هاي ديفرانسيل , روش معدل گيري , سيكل حدي , انتگرال پذيري , سيستم هاي ديفرانسيل چند جمله اي
استاد داور :
حميدرضا ظهوري زنگنه، رسول كاظمي
تاريخ ورود اطلاعات :
1396/11/03
چكيده انگليسي :
Averaging methods of arbitrary order periodic solution and integrability Nahid Bakrani nahid bakrani@math iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 34A34 34C29 37G15 34C05 34C23 Keywords Differential systems Averaging method Limit cycle Integrability Polynomial differ ential systems Abstract In this thesis we provide an arbitrary order averaging theory for higher dimensional periodicanalytic differential systems This result extends and improves results on averaging theory of periodicanalytic differential systems and it unifies many different kinds of averaging methods Applying our theory to autonomous analytic differential systems we obtain some conditions on theexistence of limit cycles and integrability For polynomial differential systems with a singularity at the origin having a pair of pure imaginaryeigenvalues we prove that there always exists a positive number N such that if its first N averagingfunctions vanish then all averaging functions vanish and consequently there exists a neighborhoodof the origin filled with periodic orbits Consequently if all averaging functions vanish the origin is acenter for n 2 Furthermore in a punctured neighborhood of the origin the system is C completely integrable forn 2 provided that each periodic orbit has a trivial holonomy Finally we develop an averaging theory for studying limit cycle bifurcations and the integrability ofplanar polynomial differential systems near a nilpotent monodromic singularity and some degeneratemonodromic singularities To know when a differential system has or not periodic solutions is very important for understandingits dynamics Averaging theory is a good theory for studying the periodic solutions Of course theaveraging theory is a classical tool for studying the behavior of nonlinear differential systems Thistheory has a long history that starts with the works of Lagrange and Laplace who work with it
استاد راهنما :
رسول عاشقي
استاد داور :
حميدرضا ظهوري زنگنه، رسول كاظمي
