13144

11994

كارشناسي ارشد

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۶

[ده]، [۱۰۵]ص.: مصور، جدول، نمودار

رضا مزروعي سبداني

انگليسي به فارسي

رضا خوش سير، مجيد گازر

1396/11/03

كتابنامه

علوم رياضي

رياضي

ID11994

Bifurcations of the Hamiltonian Fourfold 1 1 Resonance with Toroidal Symmetry Behnaz Jannesari behnaz jannesari@math iut ac ir January 8 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir 2010 MSC 37S20 37S15 53D20 53D05 53D17 70H33 70H12 34C14 Keywords Hamiltonian system Fourfold 1 1 resonance Bifurcation Normal form Re duction Hamiltonian Hopf bifurcation AbstractThis thesis is organized by paper 22 As we are seeing in introduction of this paper thisthesis deals with the analysis of Hamiltonian Hopf as well as saddle center bifurcations in4 DOF systems defined by perturbed isotropic oscillators 1 1 1 1 resonance in the pres ence of two quadratic symmetries and L1 When we normalize the system with respect tothe quadratic part of the energy and carry out a reduction with respect to a three torus groupwe end up with a 1 DOF system with several parameters on the thrice reduced phase space Then we focus our analysis on the evolution of relative equilibria around singular points ofthis reduced phase space In particular dealing with the Hamiltonian Hopf bifurcation the geometric approach is used In order to see the interplay between integrals and physicalparameters in the analysis of bifurcations we consider as a perturbation a one parameterfamily which in particular includes one of the classical Stark Zeeman models parallel case in three dimensions To be more precise on R8 with the standard symplectic form consider

رضا مزروعي سبداني

رضا خوش سير، مجيد گازر