Integrable systems in Hamiltonian mechanics and Poisson Lie groups

3 EC

Semester 2, period 6

5334ISIH3Y

Owner Master Mathematics
Coordinator prof. dr. Nicolai Reshetikhin
Part of Master Mathematics, year 1

Course manual 2018/2019

Course content

A Hamiltonian system is dynamical systems on a symplectic manifold (phase space) where the trajectories are flow lines of a Hamiltonian vector field (generated by a function known as the Hamiltonian). The Hamiltonian system on a 2n-dimensional phase space is called integrable if the there are n conserved quantities (integrals). This notion admits an important generalization known as superintegrability (degenerate integrability). The course will focus on geometry of integrable system, on some important examples and on the construction of integrable systems from Poisson Lie groups.

Study materials

Literature

  • See section "Literature on Integrable systems" on
    my Berkeley website https://math.berkeley.edu/~reshetik/

Objectives

When the course is successfully completed students are expected to learn the basics of classical integrable systems: elements of symplectic geometry with emphases on the Hamiltonian reduction, Liouville integrable Hamiltonian systems on symplectic manifolds, superintegrable systems (degenerate integrability), Poisson Lie groups, construction of integrable
systems from Poisson Lie groups.

Teaching methods

  • Lecture

Learning activities

Activity

Hours

Self study

84

Total

84

(3 EC x 28 uur)

Attendance

The programme does not have requirements concerning attendance (OER-B).

Assessment

Item and weight Details

Final grade

Assignments

Regular homework exercises and a final written exam.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

WeeknummerOnderwerpenStudiestof
1
2
3
4

Contact information

Coordinator

  • prof. dr. Nicolai Reshetikhin