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Perturbation methods for dynamical systems and Hamiltonian equations (reading course)

Number of credits: 8 hp

Examiner: Hans Lundmark and Stefan Rauch

Course literature: 1) Verhulst, F. - Nonlinear Differential Equations and Dynamical Systems (Springer 1990). Ch. 9 Introduction to perturbation theory. Ch. 10 The Poincare-Lindstedt method. Ch. 11 The method of averaging. Ch. 15 Hamiltonian systems.
2) Olver, P.J. - Applications of Lie Groups to Differential Equations (2nd ed. Springer 2000). Ch. 6 Finite-dimensional Hamiltonian systems.

Course contents: Basic concepts of perturbation theory. Poincare expansion theorem. The Poincare-Lindstedt method. The method of averaging in the periodic case. Averaging in the general case. Adiabatic invariants. Poisson brackets. Hamiltonian vector fields. Symplectic structures and foliations. Darboux's theorem. First integrals.

Organisation: Home reading and discussion with examiner, written summary of main theorems, presentation at a seminar.

Examination: Preparation of material for presentation at internal seminars. Discussion of theorems and proofs.

Prerequisites: Undergraduate education in mathematics.

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Last updated: 2022-11-15