Normal forms for nonautonomous differential equations

Abstract

We extend Henry Poincarés normal form theory for autonomous differential equations x = f(x) to nonautonomous differential equations ̇x = f(t, x). Poincarés nonresonance condition nonresonance condition λj∩ ∑ni=1ℓiλi =∅ for spectral intervals. © 2002 Elsevier Science.