MU:MU03266 Intro to Hamiltonian Systems - Course Information
MU03266 Introduction to Hamiltonian Systems
Mathematical Institute in OpavaWinter 2024
The course is not taught in Winter 2024
- 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.
- - Poisson brackets, Poisson and symplectic structures on smooth manifolds, Darboux theorem.
- 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
- 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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