13163

12011

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۶

[هفت]، [۸۳]ص.: مصور

رضا مزروعي سبداني

انگليسي به فارسي; فارسي به انگليسي

رضا خوش سير، مجيد گازر

1396/11/08

كتابنامه

علوم رياضي

رياضي

ID12011

On A Class Of The Degenerate C Neumann System Symmetry Reduction And Convexity Mohammad Hassan Malekan h malekan@math iut ac ir 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir 2010 MSC 37J15 37J35 53D20 70H06 70H33 Keywords Superintegrable system Symmetry reduction Separating co ordinates Convexity Abstract The C Neumann system is one of the few examples of an integrable system with n degrees offreedom where n is an arbitrary positive integer It describes a particle moving on the sphere S nunder the in uence of a potential that is a quadratic form In general this quadratic potential V x 1 2 x Ax x Rn 1 of the system embedded in Rn 1 has n 1 distinct eigenvaluesa0 a1 an where the degenerate case in which the eigenvalues a0 a1 an are not alldistinct is considered here in other words this is a quadratic form which has l 1 distinct eigenvaluesb0 bl of multiplicities m0 ml The Neumann system has a rotating symmetry group between coordinate axes In general thissystem is de ned on the sphere S n in Euclidean space Rn 1 and its potential matrix has n 1eigenvalues a0 an hence symmetry group of the system in this case is a direct product of n 1factors Z2 O 1 which yields the discrete Zn 1 2 However in degenerate case each group of m 0 l with equal eigenvalues gives rise toan O m symmetry in con guration space in fact for each group of m with equal eigenvalues wehave an O m symmetry that acts by rotation of the corresponding group of co ordinates So thesymmetry group in this case is G O m0 O ml

رضا مزروعي سبداني

رضا خوش سير، مجيد گازر