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273027 Introduction to Dynamical Systems 2012 (5 sp)
The course treats fundamental notions in the theory of discrete-time dynamical systems, such as periodicity, attraction/repulsion, bifurcations, chaos and sensitive dependence on initial conditions ("the butterfly effect"). In the multidimensional case we give a survey of classical stability theory for linear systems.
The course in given, in English or Swedish depending on the audience, by professor Göran Högnäs on Mondays 10-12 in aud. Vectorrummet, Tuesdays 13-15 and Fridays 13-15 in aud. Hilbertrummet B329
on the 3rd floor of the ASA building.
The course starts on Monday, January 9 at 1 p.m. and ends on Friday, March 9. There are weekly exercise sessions, but in addition some larger individual project work will also be assigned. The examination is a 24-hour open-book examination. Preliminary examination date is Thursday-Friday, March 8-9.
Prerequisites: Calculus and some course in linear algebra (matrices) and differential equation.
Course material: R. L. Devaney: An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 2nd ed. 1989 (or later editions). Additional handouts will be distributed.
The handouts can now be downloaded as pdf-files below:
A1-10 contains preliminary material from Calculus needed in the course.
Hemarbete B 28 februari.
CentralaBegrepp important notions.
Pictures of periods
On Intervals, Transitivity = Chaos by Vellekoop and Berglund
Terminology and exercises. Some exercises from the book.
More course material:
Teaching material from 2009
A picture of an Allee model
Bifurcation diagrams for the logistic model: the interval (3, 3.2), the interval (3, 3.6) and the interval (3.8, 4)
Bifurcation diagram for the Ricker model
The behaviour of the deterministic Ricker model, fixed point 57 and fixed point 1900
Approximation formula for iterations of sin(x)
Senast uppdaterad: 11.01.2012