Bifurcation Theory

Code:

M572

Acronym:

M572

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
IUD-M	2	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

Suitable for English-speaking students

Objectives

Acquaint students with results  and methods of bifurcation theory

Learning outcomes and competences

At the end of the course students should be capable of analysing qualitative changes in the dynamics arising from modifications in parameters  of differential and difference equations.

Working method

Presencial

Program

Study of qualitative changes in the dynamics arising from modifications in parameters  of differential and difference equations.
The course will deal with geoemtrical and dynamical aspects, using tools from real analysis, from topology and, for systems with symmetry, from algebra.

Mandatory literature

H. W. Broer; Structures in dynamics. ISBN: 0-444-89257-5
John Guckenheimer; Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. ISBN: 0-387-90819-6

Complementary Bibliography

Martin Golubitsky; The symmetry perspective. ISBN: 3-7643-6609-5
Michael Field; Lectures on bifurcations, dynamics and symmetry. ISBN: 0-582-30346-X

Teaching methods and learning activities

Supervised reading. Presentation of results both by the lecturer and by the students. Treatment of examples proposed to students.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	50,00
Trabalho escrito	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	143,00
Frequência das aulas	60,00
Trabalho escrito	40,00
Total:	243,00

Eligibility for exams

presence in classes

Calculation formula of final grade

sum of the marks for oral presentations (0 to 10) and homework or exam (0 to 10)