Dynamical System 2
A.Y. 2024/2025
Learning objectives
The main learning objective of the course is to prived the students with the geometrical and symmetry techniques for the study of dynamical systems in finite or infinite dimension.
Expected learning outcomes
At the end of the course, students will have acquired the ability to use the main geometrical and symmetry techniques for the study of dynamical systems in finite or infinite dimension.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
The contents of the course change depending on the knowledge and the interests of students. The first part (points 1-4 below) is usually always covered; the second part is chosen once the interest of those attending lectures are known. The following is a list of topics studied in the last editions of the course, only a part of this will be covered.
· Lie Groups
· The method of characteristics
· The geometrical meaning of a differential equation
· Symmetry and reduction of a differential equation
· Bifurcation theory
· Symmetry in variational problems
· Lax systems
· Integrable systems
· Vector fields and forms
· Differential equations in Pfaff form
· Symmetry of differential equations in the Pfaff formalism
· Frobenius theorem for vector fields
· Frobenius theorem for forms
· Gauge theories and the Higgs mechanism
· Stochastic equations and their symmetries
· Lie Groups
· The method of characteristics
· The geometrical meaning of a differential equation
· Symmetry and reduction of a differential equation
· Bifurcation theory
· Symmetry in variational problems
· Lax systems
· Integrable systems
· Vector fields and forms
· Differential equations in Pfaff form
· Symmetry of differential equations in the Pfaff formalism
· Frobenius theorem for vector fields
· Frobenius theorem for forms
· Gauge theories and the Higgs mechanism
· Stochastic equations and their symmetries
Prerequisites for admission
The student is assumed to know the subject of the mandatory courses of the "laurea triennale" (B.Sc.)
Teaching methods
Traditional lectures and autonomous study
Teaching Resources
There will be lecture notes (and additional material).
For the first part of the course:
P.J. Olver, Application of Lie groups to differential equations, Springer 1986
For the first part of the course:
P.J. Olver, Application of Lie groups to differential equations, Springer 1986
Assessment methods and Criteria
Oral examination
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Gaeta Giuseppe
Shifts:
Turno
Professor:
Gaeta GiuseppeProfessor(s)