He examined Birkhoff 's work on perturbation theory solutions for analytical Hamiltonian differential equations near an equilibrium point using formal power series. Siegel gave examples of systems which did not possess convergent transformations into a normal form.
Siya napagmasdan Birkhoff 's trabaho sa ligamgam theory solusyon para sa analytical Hamiltonian kaugalian equation na malapit sa isang punto ng balanse point gamit ang pormal na kapangyarihan ng serye. Siegel ibinigay na halimbawa ng system na hindi makamtan transformations nagtatagpo sa isang normal na form.