9468

8750

كارشناسي ارشد

علوم رياضي - رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

نه،64ص.: مصور

ص.ع.به فارسي و انگليسي

رسول عاشقي

مجيد گازر

21/10/93

حميدرضا ظهوري زنگنه، اعظم اعتماد

رياضي

ID8750

Compacti cation and desingularization of spaces of polynomial Lienard equations MohamadAli Purianejad ma purianejad@math iut ac ir 27 10 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir Advisor Dr Majid Gazor mgazor@cc iut ac ir 2010 MSC 34C07 34C20 34D10 34D15 Keywords Li nard equation Hilbert s 16th problem Limit cycle Compacti cation Desingular ization Hamiltonian perturbation Singular perturbation Abstract This thesis deals with polynomial Li nard equations of type m n i e planar vector eldsassociated to a scalar second order di erential equation x f x x g x 0 with f and g polynomials of respective degree m and n The functions f x and g x are called friction term and forcingterm respectively It is shown that besides compactifying the phase plane or the Li nard plane onecan also compactify and desingularize the space of Li nard equations of type m n for each m n separately by adding both singular perturbation problems and Hamiltonian perturbation problems Polynomial Li nard equations occur as models or at least as simpli cations of models in many domainsin science For an example during the development of radio and vacuum tube technology Li nardequations were intensely studied as they can be used to model oscillating circuits The Van der Poloscillator equation is a Li nard equation as given below d2 x dx 1 x2 x 0 2 dt dtAs put forward by Smale in his list of problems for the 21st century see 8 they are also a goodstarting point to try to solve the second part of Hilbert s 16th problem asking for a uniform upperboundonly depending on the degree for the number of limit cycles of polynomial planar vector elds

رسول عاشقي

مجيد گازر

حميدرضا ظهوري زنگنه، اعظم اعتماد