Lecture 7: Iterated function systems of linear expanding and contracting maps on the unit interval

 This lecture was presented by Prof Ale Jan Homburg (Amsterdam)

Reading material: 

• A.J. Homburg, C. Kalle. Iterated function systems of affine expanding and contracting maps on the unit interval.

Related video (recording of online seminar, see also https://www.irif.fr/~numeration/OWNS for slides). 

Lecture 6: correspondence theorem

Presentation by Matheus Manzatto de Castro 

Video recording (2022): lecture 3 (Matheus Manzatto de Castro) 

Reading material:

1. RDS - Correspondence theorem (lecture slides) 

Lecture 5: Random unstable manifolds

Presentation by Giuseppe Tenaglia.

  Video recording (2022): lecture 6  (Giuseppe Tenaglia) 

Reading material:

1. Random unstable manifolds (lecture notes)

Lecture 4: Random circle maps

 Video recording (2022): lecture  (Jeroen Lamb) 

Reading material:

1. Random circle homeomorphisms (lecture sides 2023)
2. Synchronisation in random circle maps (notes by Julian Newman)

Related material (as mentioned in class):

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 3: Minimal invariant sets

 This lecture is given by Konstantinos Kourliouros.

Reading material:

1. lecture slides
2. PhD thesis Wei Hao Tey (2022)
3. Lamb, Rasmussen, Rodrigues.  Topological bifurcations of minimal invariant sets for set-valued dynamical systems. Proc AMS 143 (2015), 3927-3937.
4. H. Zmarrou, A. J. Homburg, Bifurcations of Stationary Measures of Random Diffeomorphisms, Ergodic Theory Dynam. Systems, 27(5), (2007), 1651-1692

Lecture 2: Intermittency

This lecture is given by Bernat Bassols Cornudella.

Reading material:

1. Intermittency in iterated function systems and Infinite Ergodic Theory
: The random logistic map (RDSET project 2021)
2. Infinite Ergodic Theory and Intermittency of a random logistic map (lecture slides)
3. Neda Abbasi, Masoumeh Gharaei, and Ale Jan Homburg. Iterated functionsystems of logistic maps: Synchronization and intermittency.Nonlinearity,31(8):3880–39

Video recording (2022): panopto  

Lecture 1: The chaos game

Relevant reading material:

1. RDSETL1-slides.pdf
2. IFS-as-RDS.pdf (Jan Stanczuk, 2019)

Video recording 2022: lecture 1 (Jeroen Lamb) 

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