13252

12084

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۸۹

[هشت]، [100]ص.:‌ مصور

رضا مزروعي سبداني

رضا خوش سير قاضياني، امير هاشمي

1396/11/28

كتابنامه

علوم رياضي

رياضي

ID12084

Equivariant singularity analysis of Hamiltonian systems with the 2 2 resonance Ahmad Reisy Nafchi a reisy@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir 2010 MSC 34C29 34C99 34J40 Keywords singularity theory Gr bner basis deformation AbstractWe consider the problem of determining the phase space structure of a Hamiltonian describing a 2 2resonance With this we mean a Hamiltonian dynamical system close to an equilibrium with almostequal unperturbed positive frequencies and which is invariant with respect to reflection symmetriesin both symplectic variables in addition to the time reversion symmetry We aim at a general un derstanding of the bifurcation sequences of periodic orbits in general position from to normal modes parametrized by an internal parameter the energy and by the physical parameters the independentcoefficients characterizing the nonlinear perturbation and a detuning parameter associated with thequadratic unperturbed Hamiltonian Among low order resonances see e g 39 the symmetric 1 1 resonance plays a prominent role The general treatment is attributed to Cotter 11 in his PhD thesis but several other works exploredits generic features 5 37 38 42 Particular emphasis has been given to the symmetric subclass whichis the subject of this thesis In particular we recall the works of Kummer 29 Deprit et al 17 18 32 and Cushman and Rod 16 The connection of equivariant singularity theory and bifurcation ofperiodic orbits was made for the first time in 21 for Z2 equivariance and in 40 for S1 equivariance Broer et al 5 exploit equivariant singularity theory with distinguished parameters to study resonantHamiltonian systems We proceed on the same ground to detail the application of an equivariantsingularity analysis to the generic unfolding of a detuned 1 1 resonance invariant under Z2 Z2mirror symmetries in space and reversion symmetry in time Among several areas of application in physics chemistry and engineering there is great relevancein the application of resonance crossing to galactic dynamics 1 45 recent treatments have been given

رضا مزروعي سبداني

رضا خوش سير قاضياني، امير هاشمي