Linear systems; Nonlinear systems. Local Theory. The existence and uniqueness theorem. The flow defined by a differential equation. Linearization; The stable variety theorem. Lyapunov stability theorems. Saddles, nodes, focuses, and centers; Linearization theorems. Hartman Grobman's Theorem; Poincaré's transformation. Poincaré Bendixson's Theorem. The Poincaré sphere and the behavior of solutions at infinity.
- Differential Equations and Dynamical Systems, por Lawrence Perko
- Hirsch & Smale Diffrentiable Dynamical Systems
- Morris Hirsch; Stephen Smale. Differential Equations, Dynamical Systems and Linear Algebra. Academic Press