پديد آورنده :
بخشعلي زاده بادكي، علي
عنوان :
معيار چبيشف براي انتگرال هاي آبلي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه،126ص.: نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
حميدرضا ظهوري زنگنه
تاريخ نمايه سازي :
15/10/92
استاد داور :
مجيد گازر، رضا مزروعي سبداني
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
A Chebyshev Criterion For Abelian Integrals Ali Bakhshalizadeh Badaki a bakhsh@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir Advisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 34C07 34C08 Keywords Bifurcation Abelian integral Limit cycle Heteroclinic loop AbstractThis thesis deals with the bifurcations of limit cycle by perturbing some Hamiltonian systems Inmany applications the number and positions of limit cycles are important to understand the dynam ical behavior of the system Using the idea of Poincar map and associated displacement functionbuilt on a proper segment transversal to the period annulus of the unperturbed system the problemis reduced to the problem of nding maximum numbers of isolated zeros of some special Abelianintegral so called rst order Melnikov function We present a criterion based on papers by M Grau F Ma osas and J Villadelprat 15 31 that pro vides an easy su cient condition in order for a collection of Abelian integrals to have the Chebyshevproperty This condition involves the functions in the integrand of the Abelian integrals and can bechecked in many cases in a purely algebraic way Using this criterion several known results areobtained in a shorter way and some new results which could not be tackled by the known standardmethods can also be deduced In the literature there are many papers dealing with zeros of Abelianintegrals In many cases it is essential to show that a collection of Abelian integrals has some kind ofChebyshev property The techniques and arguments to tackle these problems are usually very long andhighly non trivial For instance in some papers the authors study the geometrical properties of theso called centroid curve using the fact that it veri es a Riccati equation which itself is deduced froma Picard Fuchs system In other papers the authors use complex analysis and algebraic topology analytic continuation argument principle monodromy Picard Lefschetz formula etc Certainly
استاد راهنما :
حميدرضا ظهوري زنگنه
استاد داور :
مجيد گازر، رضا مزروعي سبداني
