First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
SYMPLECTIC MECHANICS
SC02119743, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
N0
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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 http://matematica.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA

Lecturers
Teacher in charge FRANCO CARDIN MAT/07

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC02119743 SYMPLECTIC MECHANICS FRANCO CARDIN SC1172

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

Mode of delivery (when and how)
Period First semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 3.0 24 51.0 No turn
Lecture 3.0 24 51.0 No turn

Calendar
Start of activities 02/10/2017
End of activities 19/01/2018

Syllabus
Prerequisites: Elementary Calculus and Geometry
Target skills and knowledge: Differential and Symplectic Geometry. Global Hamiltonian Mechanics. 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.
Cohomology.
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 & Mechanics, in press, ask the author.
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, --.
  • 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