
Course unit
DYNAMICAL SYSTEMS (MOD. B)
INP5070521, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
Integrated course for this unit
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/07 
Mathematical Physics 
6.0 
Course unit organization
Period 
Annual 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
16 
34.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
Examination board
Examination board not defined
Common characteristics of the Integrated Course unit
Prerequisites:

Basic courses in Mathematical Analysis, Linear Algebra, Geometry,
Analytic Mechanics (Newton's equation, conservative force fields, potential energy, Lagrangian Mechanics). 
Target skills and knowledge:

Objectives: Introduce the students to mathematical tools in continuum mechanics and dynamical systems.
Outcomes: a student who has met the objectives of the course will have a knowledge of :
• advanced topics in the mathematical description of continuous mechanics
• fundamentals of ODEs and dynamical systems, with special emphasis on applications 
Examination methods:

Final examination based on: Written and oral examinations
on both moduli CONTINUUM MECHANICS (MOD. A) and
DYNAMICAL SYSTEMS (MOD. B).
The final evaluation will be the weighted average of the evaluations obtained in the two moduli. 
Assessment criteria:

Critical knowledge of the course topics. Ability to present the studied material. Discussion of students' projects. 
Specific characteristics of the Module
Course unit contents:

1) Ordinary differential equations: Cauchy theorem, phasespace flow, dependence on the initial conditions; linear equations; phaseportraits, first integrals; equilibrium points; linearizations, stable, center and unstable spaces.
2) Hamiltonian systems: Legendre transformation, Hamilton's equations, Poisson brackets, canonical transformations.
3) Integrable systems: elementary examples from population dynamics, from Mechanics and from Astronomy; integrability of Hamiltonian systems, LiouvilleArnold theorem, actionangle variables, examples.
4) Nonintegrable Systems: discrete dynamical systems, Poincaré sections; bifurcations, elementary examples. Stable and Unstable manifols, homoclinic chaos; Lyapunov exponents, the forced pendulum and other examples; Center manifolds and partial hyperbolicity. The three bodyproblem, the Lagrange equilibria,
Lyapunov orbits, the tube manifolds.
5) Examples and Applications: analysis of three and four dimensional systems; the Lorenz equation, the threebody problem; examples from fluid dynamics, non autonomous dynamical systems, chaos indicators, Lagrangian Coherent Structures. 
Planned learning activities and teaching methods:

Classroom lectures and exercises. Lectures are given in English. 
Additional notes about suggested reading:

"Lecture notes in Dynamical Systems" by M. Guzzo available through the Moodle website of the course on the elearning platform of the DICEA (https://elearning.unipd.it/dicea/). 
Textbooks (and optional supplementary readings) 

Massimiliano Guzzo, Lecture notes in Dynamical Systems. : , 2019. Available to regostered users through the Moodle website of the course on the elearning platform of the DICEA (https://elearning.unipd.it/dicea/)

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex
 Mathematica
 Simulations in Fortran
Sustainable Development Goals (SDGs)

