Dynamical Systems

2015 Lecture notes:

Homeomorphisms of the circle

Denjoy theory

Expanding maps of the circle

Interval maps

Topological Markov chains and the horseshoe

Coding linear torus maps

Counting words, entropy and shadowing

2015 Example sheets:

Example Sheet 1

Example Sheet 2

Example Sheet 3

Example Sheet 4

Example Sheet 5

Example Sheet 6

Lecture notes from 2014:

Notes from lecture 1

Notes from lecture 2

Notes from lectures 3 and 4

Notes from lecture 5

Notes from lecture 6

Notes from lecture 7

Notes from lecture 8

Notes from lecture 9

Notes from lecture 10

Notes from lecture 11

Notes from lecture 12

Notes from lecture 13

Notes from lecture 14

Notes from lecture 15

Notes from lecture 16&17

Notes from lectures 18&19

Correction: In the the notes of lectures 18&19 I use the word "transitive matrix" in place of "irreducible matrix".

Notes from lectures 20&21

Notes from lecture 22

Notes from lectures 23&24

Notes from lecture 25

Notes from lecture 26

Notes from lecture 27

Additional notes from lecture 27

Pictures from Wikipedia to accompany the last lecture:

Arnold tongues

Quadratic bifurcations

Mandelbrot set

Previous iterations of the course:

Lecture notes from 2013