M8240 Symplectic geometry

Faculty of Science
Spring 2015
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Anton Galaev, Dr. rer. nat. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 M6,01011
Prerequisites
Before enrolling this course the students should go through M5130 Global analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to familiarize students with the foundations of Symplectic geometry and its applications to the analysis of the problems of classical mechanics.
Syllabus
  • configuration and phase space of mechanical system,
  • Euler-Lagrange equation, Lagrange transformation, Hamilton equation,
  • symplectic manifold,
  • Darboux theorem,
  • skew-gradient,
  • Poisson bracket,
  • Hamiltonian vector field,
  • first integral of Hamiltonian systems,
  • Emmy Noether theorem,
  • complete integrability by Liouville
Literature
    recommended literature
  • J.Podolský, Teoretická mechanika v jazyce diferenciální geometrie. Praha 2006. http://utf.mff.cuni.cz/vyuka/TMF069/tmf069.pdf
  • ARNOL'D, Vladimir Igorevič. Mathematical methods of classical mechanics. 2nd ed. New York: Springer-Verlag, 1989, ix, 516 s. ISBN 0-387-96890-3. info
  • Fomenko, A. T.; Trofimov, V. V. Integrable systems on Lie algebras and symmetric spaces. Advanced Studies in Contemporary Mathematics, 2. Gordon and Breach Science Publishers, New York, 1988. xii+294 pp. ISBN: 2-88124-170-0
  • Arnolʹd, V. I.; Giventalʹ, A. B. Symplectic geometry. Dynamical systems, IV, 1–138, Encyclopaedia Math. Sci., 4, Springer, Berlin, 2001.
Teaching methods
Standard lectures aimed at the explanation of the theory.
Assessment methods
oral final exam
Language of instruction
Czech
Further Comments
Study Materials
The course is taught only once.
  • Enrolment Statistics (recent)
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