Related to the Cambridge Part II Dynamical Systems course
Final chapter of the course, on chaotic dynamics
(with an emphasis on symbolic dynamics) PDF format.
The following draw heavily on previous versions put together by John Lister, Mike Proctor and probably others. Errors, omissions etc are of course my responsibility...
A brief discussion of unimodal maps, with many colour figures. PDF format.
Centre manifolds. PDF format.
These last few are in some places lacking figures. Readers are encouraged to add relevant sketches to the text!
Topological equivalence and structural stability for flows. PDF format.
Basins of attraction. PDF format.
Reduction to normal form near a Hopf bifurcation. PDF format.
Proof of the Poincare-Bendixson theorem. PDF format.
Related to Cambridge Part III courses on nonlinear dynamics
Introductory concepts in dynamical systems. Gzipped postscript or PDF formats.
The Kuramoto-Sivashinsky Equation. Gzipped
postscript or PDF formats. This refers
frequently to pictures handed out in the lecture.
INI programme: Pattern Formation in Large Domains -- Training Course: Pattern Formation, 1-5 August 2005
Notes on local bifurcations with symmetry.
Lecture 1: Groups, representations and linear theory. Gzipped postscript or PDF formats.
Lecture 2: Amplitude equations and Hopf bifurcations. Gzipped postscript or PDF formats.
Lecture 3: From PDEs to ODEs. Gzipped postscript or PDF formats.
Lecture 4: Heteroclinic cycles and networks. Gzipped postscript or PDF formats.
References: Gzipped postscript or PDF formats.
Problems: Gzipped postscript or PDF formats.
Answers to problems: Gzipped postscript or PDF formats.
Preliminary Course for Part IA, September 2006
Limits and Series.
Lecture Notes: Gzipped postscript or PDF formats.
Problem Sheet: Gzipped postscript or PDF formats.
Problem Sheet with answers and comments: Gzipped postscript or PDF formats.