Hyperbolic Dynamics

Code:

M518

Acronym:

M518

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 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	1	PE do Prog Inter-Univ Dout Mat	1	-	9	60	243

Teaching language

English

Objectives

To study local and global properties of dynamical systems whose behavior is not affected by small perturbations (stable systems). To classify those systems according to the geometric and topological features of their basic sets.

Learning outcomes and competences

To identify hyperbolicity in discrete-time and continuous-time dynamical systems.

Working method

Presencial

Program

1 - Linear systems
2 - Local stability
3 - Invariant manifolds and the inclination lemma
4 - Hyperbolic sets
5 - Spectral decomposition
6 - Markov partitions and codification

Mandatory literature

Palis Jr. Jacob; Geometric theory of dynamical systems. ISBN: 0-387-90668-1
Irwin M. C.; Smooth dynamical systems. ISBN: 0-12-374450-4
Robinson Clark; Dynamical systems. ISBN: 0-8493-8495-8
Shub Michael; Global stability of dynamical systems. ISBN: 0-387-96295-6
Brin Michael; Introduction to dynamical systems. ISBN: 0-521-80841-3

Teaching methods and learning activities

Presentations with shalk and blackboard.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

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

Calculation formula of final grade

Classification of an oral presentation and written notes.