پديد آورنده :
نصرآزاداني، زهرا
عنوان :
سيكل پذيري كانون ساده از طريق مرتبه تكرار صفر عامل هاي انتگرال ساز وارون
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
رسول عاشقي
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
مركز , سيكل هاي حدي
تاريخ نمايه سازي :
1394/10/26
استاد داور :
حميدرضا ظهوري زنگنه، اعظم اعتماد
چكيده انگليسي :
Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors Zahra Nasr Azadani zahra nasr@math iut ac ir 23 12 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 34C07 37G10 37G15 Keywords Focus Center Inverse integrating factor Cyclicity of a focus Limit cycles Vanishingmultiplicity Abstract First we provide new properties about the vanishing multiplicity of the inverse integrating factorof a planar analytic di erential system at a focus After we use this vanishing multiplicity for studyingthe cyclicity of foci with pure imaginary eigenvalues and with homogeneous nonlinearities of arbitrarydegree having either its radial or angular speed independent of the angle variable in polar coordinates After we study the cyclicity of a class of nilpotent foci in their analytic normal form We present an alternative algorithm for computing Poincar Lyapunov constants of simple mon odromic singularities of planar analytic vector elds based on the concept of inverse integrating fac tor Simple monodromic singular points are those for which after performing the rst generalized polar blow up there appear no singular points In other words the associated Poincar return mapis analytic We study the maximum number of limit cycles that can bifurcate from a focus singular point p0 ofan analytic autonomous di erential system in the real plane under an analytic perturbation Weconsider p0 being a focus singular point of the following three types non degenerate degenerate without characteristic directions and nilpotent In a neighborhood of p0 the di erential system can always be brought by means of a change to generalized polar coordinates r to an equation over a cylinder in which the singular point p0corresponds to a limit cycle 0 This equation over the cylinder always has an inverse integrating
استاد راهنما :
رسول عاشقي
استاد داور :
حميدرضا ظهوري زنگنه، اعظم اعتماد
