PoincaréDulac
Poincaré-Dulac refers to a foundational result in local normal form theory for analytic vector fields near a fixed point. It provides a systematic method to simplify the equations by removing nonresonant nonlinear terms through near-identity changes of coordinates, leaving only resonant nonlinearities that reflect the intrinsic structure of the linear part.
Statement and key ideas: Consider a system x' = A x + f(x) in a neighborhood of 0, with
Convergence and implications: In the analytic (convergent) category, convergence of the normalization depends on arithmetic properties
See also: normal form theory, linearization, resonance, small divisors.