Course: Variational Analysis II

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Course title Variational Analysis II
Course code MU/04065
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
Course content
- Regular variational problems in mechanics (the regularity condition, the Legendre transformation, the canonical Hamilton equations). - Poisson and symplectic structures. Hamiltonian systems and their integrals. Integrability and the Liouville theorem. Reduction of Hamiltonian systems and the moment map. Separation of variables in Hamiltonian systems and the Hamilton-Jacobi theory. - Bihamiltonian systems and their properties. - Poisson and symplectic structures on the evolutionary system of partial differential equations and their properties. Bihamiltonian systems of PDEs and their integrability. Recursion operators.

Learning activities and teaching methods
Recommended literature
  • A. T. Fomenko. Symplectic geometry. Gordon and Breach, New York, 1988. ISBN 2881246575.
  • D. Krupka. Some Geometric Aspects of Variational problems in Fibered Manifolds. Folia Fac. Sci. Nat. Univ. Purk. Brunensis, Physica, XIV, Brno, 1973.
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963.
  • M. Giaquinta, S. Hildebrandt. Calculus of variations I and II. Springer, Berlín, 1996. ISBN 3540579613.
  • N. A. Bobylev, S. V. Emel'yanov, S. K. Korovin. Geometrical methods in variational problems. Boston, 1999. ISBN 0-7923-5780-9.
  • O. Krupková. The geometry of ordinary variational equations. Springer, Berlín, 1997. ISBN 3540638326.
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993.
  • V. I. Arnold. Mathematical methods of classical mechanics. Springer, New York, 1999. ISBN 0387968903.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 5 Summer