TU Berlin Fakultät II
Institut für Mathematik

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Mathematical Physics I: Dynamical Systems and Classical Mechanics   (WS 11/12)


Lectures   Dr. Matteo Petrera Mon  12:15 - 14:00  MA 750
  Dr. Matteo Petrera  Fri  12:15 - 14:00  MA 750
Tutorial   Dr. Pasquale Zito Tue  16:15 - 18:00  MA 749

This is a course of the Berlin Mathematical School held in English.

Office hours

Name Office hours Room
Lectures   Dr. Matteo Petrera                     Wed 10:00 - 12:00   MA 819
Tutorial    Dr. Pasquale Zito     By appointment, Fri 15:30 - 17:30


  • Ordinary differential equations, Existence and uniqueness theorems, Dependence on initial conditions and parameters, Prolongation of solutions.

  • Dynamical systems (with continuous and discrete time), Flows and vector fields, Fixed points, Stability theorems, Linear dynamical systems, Linearization, Local bifurcation theory.

  • Lagrangian mechanics in R^n, Legendre Transformation, Hamiltonian mechanics in R^n, Symplectic structure of the phase space, Poisson brackets, Canonical transformations, Hamilton-Jacobi theory, Symplectic integrators, Differentiable manifolds, Mechanics on manifolds, Symmetries and Noether theorem, Symplectic geometry, Poisson geometry, Rigid body equations of motion.



Homework sheets

Class Exercises (discussed and solved in class)

  • Tutorial 1 (18.10.11) (Examples of ODEs, construction of explicit solutions)
  • Tutorial 2 (25.10.11) (Initial value problems, existence and uniqueness Theorem, maximal solutions)
  • Tutorial 3 (01.10.11) (Qualitative analysis, planar systems od ODEs, integrals of motion, integrale curves)
  • Tutorial 4 (08.11.11) (Periodic systems, discrete dynamical systems, integrals of motion, commuting flows)
  • Tutorial 5 (15.11.11) (Linear autonomous and homogeneous systems, Lyapunov functions)
  • Tutorial 6 (22.11.11) (Lyapunov functions, Poincaré-Lyapunov Theorem, Topological conjugacy)
  • Tutorial 7 (29.11.11) (Center manifolds, Bifurcations)
  • Tutorial 8 (06.12.11) (Conservative systems with one degree of freedom)
  • Tutorial 9+10 (13.12.11) (Variational problems, Hamiltonian and Lagrangian mechanics, motion in central potential)
  • Tutorial 11 (10.01.12) (Canonical transformations, Hamilton-Jacobi theory).
  • Tutorial 12 (17.01.12) (Differentiable manifolds, differentiable maps, Regular value Theorem)
  • Tutorial 13 (24.01.12) (Geodesics, Noether Theorem, symmetries)
  • Tutorial 14 (31.01.12) (Lie groups, Lie algebras, exponential map, examples)
  • Tutorial 15 (07.02.12) (Action-angle variables)

Homework policy

  • To get a certificate for the tutorial, you need to satisfactorily complete 60% of the homework assignments.
  • The homeworks are due weekly at the beginning of the Tuesday lecture (16:00). No homework will be accepted after the deadline has passed.
  • Homeworks may be turned in directly to the assistant at the lecture.

Matteo Petrera . 09.03.2012