Lecture 3: Iterated function systems with contracting and expanding maps

Guest lecture by Prof Ale Jan Homburg (University of Amsterdam and University of Leiden).

Reading material:

• ITERATED FUNCTION SYSTEMS OF AFFINE EXPANDING AND CONTRACTING MAPS ON THE UNIT INTERVAL ALE JAN HOMBURG AND CHARLENE KALLE 
• Notes: Iterated function systems on the interval with contracting and expanding maps 

Lecture 2: Random circle homeomorphisms

Video recording (2022): lecture  (Jeroen Lamb) 

Reading material:

1. Random circle homeomorphisms (lecture sides 2023)
2. Synchronisation in random circle maps (by Julian Newman - adapted extract (2026))

Other related material:

1. Necessary and Sufficient Conditions for Stable Synchronisation in Random Dynamical Systems (talk by Julian Newman @ BIRS (2015)).
2. Random product of maps synchronizing on average (E. Matias an I. Melo)
3. Random walks on Homeo(S^1) (D. Malicet)

Lecture 1: The chaos game

 Relevant reading material:

1. RDSETL1-slides.pdf (used in previous years' lectures)
2. IFS-as-RDS.pdf (Jan Stanczuk, 2019)

Chaos game app.

Video recording 2022: lecture 1 (Jeroen Lamb) 

Video recording lecture 2021: lecture 1 (passwd: rds&et2021) Jeroen Lamb