Laurea in Matematica Applicata

Dynamical Systems I (2012/2013)

Course code 4S02754 Teacher Gaetano Zampieri Coordinator Gaetano Zampieri training credits 6 Disciplinary sector MAT/07 - MATHEMATICAL PHYSICS Teaching language Italian Period II semestre dal Mar 4, 2013 al Jun 14, 2013.

Links Course news Seminars related to the course

Lecture timetable

Educational objectives

The aim of the course is to deal with the qualitative analysis of
autonomous ordinary differential equations and to introduce to the
theory of continuous dynamical systems. The student should reach the
knowledge of the theory with reasonable depth, and also some working
ability of the examples.

Syllabus

Flows. Orbits and invariant sets. First integrals. Vector fields with the same orbits. The conservative simple pendulum. The fish. Predator-prey. Bounded vector fields. Solutions in compact sets. Alfa and omega-limit sets.
Changes of variables. Local rectification theorem. Linear vector fields.
Invariance principle. Lyapunov stability theorem. Asymptotic stability
and instability from the linearization. Stability for the conservative and dissipative pendulum. Flows on the circle. Flows on the cylinder. Polar coordinates. Limit cycles. Uniform motion on the 2-torus. Systems of harmonic oscillators. A 2-torus as omega-limit of a 3-dimensional flow.

Exam methods

Oral examination.

Teaching aids
Title	Format (Language, Size, Publication date)
URL per accedere alle dispense	pdf (it, 14.779 KB, 5/27/13)

Statistics on students' past performance (Art. 2 del D.M. 31/10/2007, n. 544)

Data from AA 2012/2013 are not available yet