Lecture 8: Conditioned Lyapunov exponents for random dynamical systems

 Guest lecturer Prof Martin Rasmussen.

Lecture slides

Lecture 7: Infinite ergodic theory and intermittency in a random logistic map

Guest lecture by Dr Bernat Bassols Cornudella.

lecture slides 

Lecture 6: Random products of matrices

Guest lecture by Mr Christopher Chalhoub

Lecture notes

Lecture 5: Lyapunov exponents

Guest lecture by Dr Giuseppe Tenaglia

Reference: 

Lian, Z., & Stenlund, M. (2012). Positive Lyapunov exponent by a random perturbation.Dynamical Systems, 27(2), 239–252. https://doi.org/10.1080/14689367.2012.667787

(also https://arxiv.org/pdf/1012.4303)

Lecture 4: Attractors of RDS with bounded noise (boundary map approach)

 Guest lectures given by Wei Hao Tey and Konstantinos Kourliouros.

Material:

ATTRACTORS OF LINEAR MAPS WITH BOUNDED NOISE

Smooth Persistence of Attractors for Set-Valued Dynamical Systems: A Boundary Map Approach

Bifurcations of the Hénon Map with Additive Bounded Noise

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)