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In this program

Linearization
Hartman–Grobman theorem (statement)
Stable and unstable manifolds (introduction)
Limit cycles
Poincaré–Bendixson theorem (2D)
Hamiltonian and gradient systems (introduction)
Index theory for closed orbits (optional)

Nonlinear dynamics

Hartman–Grobman theorem (statement)

Dynamical systems · Standard syllabus

Topic

Hartman–Grobman theorem (statement)

Practice by unit: Nonlinear dynamics

Undergraduate Dynamical Systems — scope drawn from open dynamical systems notes and typical US intro dynamical systems syllabi.

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