MAGIC060: Dynamical Systems II (Maps)

Course details

A core MAGIC course

Semester

Autumn 2013
Monday, October 7th to Saturday, December 14th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Wednesdays
09:05 - 09:55

Description

The course provides an introduction to the topological dynamics of iterated maps: circle maps, unimodal maps, Smale's horseshoe, Hyperbolic toral automorphisms, and polynomials CC. There is an emphasis on symbolic techniques (kneading theory, Markov partitions, etc.)
The aim is to provide an introduction to a broad range of topics, rather than to discuss any of the topics in great depth.

Prerequisites

Undergraduate-level courses in metric spaces and complex analysis.

Syllabus

  1. One-dimensional maps, circle maps, logistic map, period doubling cascade
  2. Chaos, symbolic coding of trajectories
  3. Two or higher dimensional maps, examples: cat map
  4. Hyperbolicity, homoclinic intersections, Smale horseshoe
  5. Quadratic polynomials, Julia and Mandelbrot sets

Lecturer

  • TH

    Dr Toby Hall

    University
    University of Liverpool

Bibliography

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You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

Assessment

Description

Assessment will be by a take-home exam paper in January 2014. You will have 2 weeks to complete the exam and submit your solutions online. There will be 5 questions, and full marks can be obtained if you submit correct solutions to 3 of them.

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Files

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Lectures

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