پديد آورنده :
رضائي، الهام
عنوان :
روش معدل گيري براي معادلات ديفرانسيل قطعه اي نا پيوسته
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، [97]ص.:مصور
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
حميدرضا ظهوري زنگنه
واژه نامه :
فارسي به انگليسي; انگليسي به فارسي
توصيفگر ها :
معادلات ديفرانسيل , قضيه ي معدل گيري , اثبات قضاياي اصلي
استاد داور :
رسول عاشقي، رسول كاظمي
تاريخ ورود اطلاعات :
1396/05/30
چكيده انگليسي :
Averaging theory for discontinuous piecewise di erential systems Elham Rezaei Elham Rezaei1@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid R Z Zangeneh hamidz@cc iut ac ir 2010 MSC 37G15 37C80 37C30 Keywords Periodic solution Limit cycles averaging Discontinuous di erential systems Nonsmoothdynamical systems AbstractThis thesis has been written based on book and papers 4 7 13 In these last years a big interest hasappeared for studying discontinuous di erential systems that is di erential equations with discon tinuous right hand sides This interest has been stimulated by discontinuous phenomena in controlsystems impact and friction mechanics nonlinear oscillations economics and biology and it hasbecome certainly one of the common frontiers between Mathematics Physics and Engineering Formore details see Teixeira 21 A recent review appears in 22 One of the main problems in the qualitative theory of di erential systems is the study of theirperiodic solutions A good tool to study the periodic solutions is the averaging theory We point outthat the method of averaging is a classical and matured tool that provides a useful means to studythe behavior of nonlinear smooth dynamical systems The method of averaging has a long historythat starts with the classical works of Lagrange and Laplace who provided an intuitive justi cationof the process The rst formalization of this procedure was given by Fatou in 1928 Very importantpractical and theoretical contributions in the averaging theory were made by Krylov and Bogoliubovin the 1930s and Bogoliubov in 1945 The classical results in the averaging theory require at least that the systems are of class C 2 Nevertheless Buica and Llibre in 5 using mainly topological tools as the Broudwer degree theory extended the averaging theory up to order 3 for studying periodic orbits of continuous Lipschitzdi erential systems Their results were generalized for any order in 2014 Recently the theory of
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد داور :
رسول عاشقي، رسول كاظمي
