First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SC02119743, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination SYMPLECTIC MECHANICS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge FRANCO CARDIN MAT/07

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/07 Mathematical Physics 6.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Examination board not defined

Prerequisites: Elementary Calculus and Geometry
Target skills and knowledge: Differential and Symplectic Geometry. Global Hamiltonian Mechanics. Geometric theory of the Hamilton-Jacobi equation. Symplectic Topology. Calculus of Variations: Conjugate Points, Morse Index, Lusternik-Schnirelman Theory for the existence of critical points.
Examination methods: Written.
Assessment criteria: Assessment of learning theoretical and practical notions on the course.
Course unit contents: Essential of Differential Geometry and Exterior Differential Calculus.
Riemannian manifolds:
Existence of metrics, Whitney theorem.
Symplectic Geometry:
Symplectic manifolds.
Introduction and developments of Hamiltonian Mechanics on symplectic manifolds.
Local and global parameterization of the Lagrangian submanifolds and their
generating functions. Theorem
of Maslov-H\"ormander.
Hamilton-Jacobi equation, its geometrical solutions and links to the Calculus of
Variations. Conjugate points
theory in calculus of variations.
Relative cohomology and Lusternik-Schnirelman theory. Introduction to Symplectic
Topology: existence and classification of critical points of
functions and applications to generating functions of Lagrangian submanifolds.
The min-max solution of Hamilton-Jacobi equation. Symplectic Topology by Viterbo: towards the solution of the Arnol'd conjecture. Morse theory.
Planned learning activities and teaching methods: lectures and tutorials
Additional notes about suggested reading: F. Cardin: Elementary Symplectic Topology and Mechanics, Springer 2015
Textbooks (and optional supplementary readings)
  • Hofer, Helmut; Zehnder, Eduard, Symplectic invariants and Hamiltonian dynamics. --: Birkhäuser, 1994. Cerca nel catalogo
  • Arnolʹd, V. I., Mathematical methods of classical mechanics. Springer Verlag: 1989, --. Cerca nel catalogo
  • McDuff, Dusa, Salamon, Dietmar, Introduction to symplectic topology. --: Oxford Mathematical Monographs, 1998. Cerca nel catalogo
  • F. Cardin, Elementary Symplectic Topology and Mechanics. --: Springer Verlag, 2015. Cerca nel catalogo