عنوان :
سيكل هاي كانارد در حضور جريان هاي كند داراي نقاط تكين
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هشت، 71ص.: مصور
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
رسول عاشقي
استاد مشاور :
رضا مزروعي سبداني
توصيفگر ها :
سيكل پذيري , نقطه تاشدگي , مدارهاي كانارد , انتگرال ديورژانس كند
تاريخ نمايه سازي :
94/2/16
استاد داور :
حميدرضا ظهوري زنگنه، اعظم اعتماد
تاريخ ورود اطلاعات :
1396/09/27
چكيده انگليسي :
Canard cycles in the presence of slow dynamics with singularities Moosa Koohi moosa koohi@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir Advisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir 2010 MSC 34C05 34C07 34C23 34C26 Keywords cyclicity turning point canard orbits slow dynamics slow divergence integral Abstract We study the cyclicity of limit periodic sets that occur in families of vector elds of slow fast type The limit periodic sets are formed by a fast orbit and a curve of singularities containing a uniqueturning point At this turning point a stability change takes place on one side of the turning pointthe dynamics point strongly towards the curve of singularities on the other side the dynamics pointaway from the curve of singularities The presence of periodic orbits in a perturbation is relatedto the presence of canard orbits passing near this turning point i e orbits that stay close to thecurve of singularities despite the exponentially strong repulsion near this curve All existing resultsdeal with a non zero slow movement permitting a good estimate of the cyclicity by considering theslow divergence integral along the curve of singularities In this thesis we study what happens whenthe slow dynamics exhibit singularities In particular our study includes the cyclicity of the slow fasttwo saddle cycle formed by a regular saddle connection the fast part and a part of the curve ofsingularities the slow part We see that the relevant information is no longer merely contained inthe slow divergence integral This thesis concerns the study of the cyclicity of limit periodic sets in a quite general class ofslow fast vector elds on a 2 manifold M We are interested in families of vector elds X possiblydepending on other parameters as well where the unperturbed fast vector eld X0 has a curve ofsingular points called a critical curve We call a point p on normally attracting respectively normally repelling when DX0 p has a strictly negative respectively strictly positive eigenvalue
استاد راهنما :
رسول عاشقي
استاد مشاور :
رضا مزروعي سبداني
استاد داور :
حميدرضا ظهوري زنگنه، اعظم اعتماد
