11857

10882

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

نه، 114ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

واژه نامه

1395/09/02

كتابنامه

رياضي

ID10882

Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector elds Marziyeh Akhtari 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Prof Hamidreza Zohouri Zangeneh 2010 MSC 34C07 34C08 Keywords Hamiltonian nilpotent center Cubic polynomial Vector elds Phase portrait Abstract This thesis is based on the following paper Hamiltonian nilpotent centers of linear pluscubic homogeneous polynomial vector elds I E Colak J Llibre C Valls Determining limit cycles and distinguishing when a singular point is either a focus ora center are two of the main problems in the qualitative theory of real planar polynomialdi erential systems Poincare in 21 de nes a center for a vector eld on the real plane asa singular point having a neighborhood lled with periodic orbits with the exception of thesingular point If an analytic system has a center then after an a ne change of variables and a rescalingof the time variable it can be written in one of the following three forms x y P px yq y x Qpx yq 9 9called a linear type center x y P px yq y Qpx yq 9 9

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