MU03266 Introduction to Hamiltonian Systems

Mathematical Institute in Opava
Winter 2023

The course is not taught in Winter 2023

Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU03038 Differential Geometry I && TYP_STUDIA ( N )
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The purpose of the subject is introducing the students to the basics of symplectic and Poisson geometry and theory of Hamiltonian systems.
Syllabus
  • - Poisson brackets, Poisson and symplectic structures on smooth manifolds, Darboux theorem.
    - Integrals of motion, symmetries, Hamiltonian, Hamiltonian vector fields, Hamiltonian equations.
    - Legendre transform and relationship among Lagrangian and Hamiltonian formalism.
    - Complete integrability and Liouville's theorem.
    - Hamilton-Jacobi equations, complete integral, separation of variables.
Literature
    required literature
  • R. Berndt. An Introduction to Symplectic Geometry. AMS, 2001. info
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
    recommended literature
  • V. I. Arnold. Mathematical methods of classical mechanics. Springer, New York. ISBN 0387968903. 1999. info
  • L. D. Landau, E. M. Lifshitz. Mechanics. Pergamon Press, 1960. info
    not specified
  • M. Fecko, J. Korbaš, M. Niepel, P. Ševera. Zimná škola symplektickej geometrie. Bratislava, 2007. URL info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Attending the lectures is desirable. In the course of the first lecture the lecturer will communicate to the students the requirements regarding the conditions of successfully passing the subject. Succeeding in the fail/pass test requires attaining the score of at least 60 percent at the test papers (typically two in the semester) or 70 percent at the remedial test paper. The exact requirements and dates for submitting the papers are set by the tutor. The exam is merely oral. In its course one tests the knowledge and the skills of the students gained during the study of the subject in question.
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