His research concentrated on asymptotic expansions, boundary value problems, and Sturm - Liouville type problems but his thesis advisor Eliakim Moore appears to have been a less influential guide to Birkhoff than was Poincaré . Birkhoff read Poincaré 's works on differential equations and celestial mechanics and he learnt more, and was more strongly influenced in the direction his research was taking, by Poincaré than from his supervisor.
Ang kanyang mga pananaliksik sa puro asymptotic expansions, punta halaga ng mga problema, at Sturm - Liouville uri ng problema ngunit ang kanyang tesis taga-payo Eliakim Moore ay lilitaw na magkaroon ng isang mas hindi dominante na gabay upang was Birkhoff kaysa sa Poincaré. Birkhoff read Poincaré 's gumagana sa kaugalian equation at makalangit mechanics at siya learnt more, at noon ay mas malakas naiimpluwensyahan sa direksyon ng kanyang mga pananaliksik ay dinadala, sa pamamagitan ng Poincaré kaysa sa mula sa kanyang superbisor.