MATH 540 Dynamical Systems

Geometric theory of differential equations. Existence and uniqueness theorems; continuous dependence on initial conditions and parameters. Flows for autonomous and nonautonomous systems. Topological conjugacy and equivalence, HartmanGrobman theorem. Stability theory. Nonautonomous linear systems and Floquet theory. Periodic solutions and PoincarĂ© maps. Global methods, Liapunov theory and LaSalle invariance principle. Stable, unstable, and center manifolds. Structural stability and bifurcation theory. Symbolic dynamics and the shift map. Homoclinic phenomena.
Credit units: 3 ECTS Credit units: 5.



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