Normal Forms and Unfoldings for Local Dynamical Systems

Focusing on local dynamical systems, the book addresses two main questions: the behavior of solutions near the origin for differential equations with a linear part represented by an n×n matrix, and the behavior of systems close to this type. It outlines a method involving the derivation of a normal form for the general system, which simplifies its analysis through coordinate changes. Additionally, it discusses the unfolding of this normal form, incorporating parameters for systems nearby, and examines the truncated behavior of the resulting system.