MAGIC060: Dynamical Systems II (Maps)

Details Description Lecturer Bibliography Assessment Files Lectures

Course details

A core MAGIC course

Semester

Spring 2012: Monday, January 16th to Friday, March 23rd

Hours

Live lecture hours: 10

Recorded lecture hours: 0

Total advised study hours: 0

Timetable

Fridays: 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 C → C. 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

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

Lecturer

TH

Dr Toby Hall

University

University of Liverpool

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

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.

Please see the file "Comments on the bibliography" in the "Files" tab (, )
GENERAL TEXTS (, )
An introduction to chaotic dynamical systems (Devaney, book)
A first course in dynamics: with a panorama of recent developments (Hasselblatt and Katok, book)
Introduction to the modern theory of dynamical systems (Katok and Hasselblatt, book)
One-dimensional dynamics (de Melo and van Strien, book)
Dynamics in one complex variable: introductory lectures (Milnor, book)
TEXTS DEALING WITH SPECIFIC TOPICS (, )
Quantitative universality for a class of nonlinear transformations (Feigenbaum, msn)
A computer-assisted proof of the Feigenbaum conjectures (Lanford, msn)
A shorter proof of the existence of the Feigenbaum fixed point (Lanford, msn)
Generalizations of a theorem of Sarkovskii on orbits of continuous real-valued functions (Baldwin, msn)
Topological entropy (Adler, Konheim and McAndrew, msn)
Entropy for group endomorphisms and homogeneous spaces (Bowen, msn)
Horseshoes for mappings of the interval (Misiurewicz, msn)
Topological entropy of Devaney chaotic maps (Balibrea and Snoha, msn)
On iterated maps of the interval (Milnor and Thurston, msn)
Kneading theory (Scholarpedia, web)
Entropy of piecewise monotone mappings (Misiurewicz and Szlenk, msn)
Bifurcations in one dimension. I. The nonwandering set (Jonker and Rand, msn)
Differentiable dynamical systems (Smale, msn)
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms (Katok, msn)
A two-dimensional mapping with a strange attractor (H{\'e}non, msn)
The dynamics of the Hénon map (Benedicks and Carleson, msn)
Antimonotonicity: concurrent creation and annihilation of periodic orbits (Kan, Ko{\c{c}}ak and Yorke, msn)

Assessment

The assessment for this course will be released on Monday 21st September 2020 and is due in by Friday 27th April 2012 at 23:59.

Assessment will be by a take home exam at the end of the course. Further details will be provided in due course.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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