پديد آورنده :
ميرزايي، هاجر
عنوان :
سيكل پذيري برخي مراكز پوچتوان متقارن
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هفت، [۱۳۶]ص.: مصور
استاد راهنما :
رسول عاشقي
واژه نامه :
انگليسي به فارسي; فارسي به انگليسي
توصيفگر ها :
پايه گروبنر , سيستم هاي هاميلتوني , قطاع ها , پوانكاره - لياپانف
استاد داور :
حميدرضا ظهوري زنگنه، رسول كاظمي
تاريخ ورود اطلاعات :
1396/09/13
چكيده انگليسي :
Cyclicity of some symmetric nilpotent centers Hajar Mirzaie h n mirzaie12@gmail com 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 37G15 37G10 34C07 Keywords Monodromic singularity Nilpotent center Cyclicity Limit cycle AbstractIn this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotentsingularities of symmetric polynomial planar vector elds The starting point is identifying a broadfamily of nilpotent symmetric elds for which existence of a center is equivalent to existence of alocal analytic rst integral which unlike the degenerate case is not true in general for nilpotentsingularities We are able to relate so called focus quantities to the Poincar Lyapunov quantities arising from the Poincar rst return map When we apply the method to concrete examples weshow in some cases that the upper bound is sharp Our approach is based on computational algebramethods for determining a minimal basis constructed by focus quantities instead of by Poincar Lyapunov quantities because of the easier computability of the former of the associated polynomialBautin ideal in the parameter space of the family The case in which the Bautin ideal is not radicalis also treated Knowledge of the local qualitative phase portrait near an isolated singularity p0 R2 of a realanalytic planar vector eld X is an almost completely solved problem see for example 6 Only forthe so called monodromic singularities that problem remains open We recall that p0 is monodromicwhen nearby orbits of X rotate about p0 Also it is well known after an independent proof in 10 and 17 that monodromic singularities only can be centers having a punctured neighborhood lledwith periodic orbits or foci having a punctured neighborhood lled with spiraling orbits The centerproblem is the problem of distinguishing between a center or a focus at a monodromic singular point In this work we focus on nilpotent singularities which appear when the linear part DX p0 of X at p0 isnonzero and has two zero eigenvalues More precisely we will deal with polynomial families of planar
استاد راهنما :
رسول عاشقي
استاد داور :
حميدرضا ظهوري زنگنه، رسول كاظمي
