MU04065 Variational Analysis II

Mathematical Institute in Opava
Summer 2012
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Prerequisites
MU04064 Variational Analysis I
MU/04064
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 goal of the lectures is to introduce the students to the more advanced aspects of calculus of variations.
Syllabus
  • - 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.
Literature
    recommended literature
  • N. A. Bobylev, S. V. Emel'yanov, S. K. Korovin. Geometrical methods in variational problems. Boston, 1999. ISBN 0-7923-5780-9. URL info
  • V. I. Arnold. Mathematical methods of classical mechanics. Springer, New York, 1999. ISBN 0387968903. info
  • M. Giaquinta, S. Hildebrandt. Calculus of variations I and II. Springer, Berlín, 1996. ISBN 3540579613. info
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
  • A. T. Fomenko. Symplectic geometry. Gordon and Breach, New York, 1988. ISBN 2881246575. info
  • I. M. Gelfand, S. V. Fomin. Calculus of Variations. Englewood Cliffs, Prentice-Hall, 1963. URL info
    not specified
  • O. Krupková. The geometry of ordinary variational equations. Springer, Berlín, 1997. ISBN 3540638326. info
  • D. Krupka. Some Geometric Aspects of Variational problems in Fibered Manifolds. Folia Fac. Sci. Nat. Univ. Purk. Brunensis, Phys, 1973. 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
Oral exam; further requirements to be specified in the course of the semester.
The course is also listed under the following terms Winter 1997, Summer 1998, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2012, recent)
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