Lecture 7: Synchronization Properties of Random Piecewise Isometries

Guest lecture by Vincent Goverse.

Relevant paper:

Gorodetski, A., Kleptsyn, V. Synchronization Properties of Random Piecewise Isometries. Commun. Math. Phys. 345, 781–796 (2016).

Lecture 6: Attractors for systems with bounded noise.

 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
5. Lamb, Rasmussen, Tey. Attractors of linear maps with bounded noise

Lecture 5: random circle homeomorphisms

 Slides

Lecture notes by Julian Newman (2017)

recommended literature (advanced):  Random walks on Homeo(S^1) (D. Malicet)

Lecture 4: correspondence theorem

Guest lecture by Matheus Manzatto.

Relevant notes (by Martin Rasmussen) provided on black board.

Lecture 3: intermittence and infinite ergodic measures

Guest lecture by Bernat Bassols Cornudella.

Slides

Relevant literature:

• N. Abbasi, M. Gharaei, A.J. Homburg. Iterated function systems of logistic maps: synchronization and intermittency. Nonlinearity 31, 3880-3913. [doi]
• R. Zweimuller. Notes on infinite ergodic theory. 2009
• B. Bassols-Cornudella. Intermittency in iterated function systems and Infinite Ergodic Theory: the random logistic map. RDS&ET project 2021

Lecture 2: heterochaos baker map

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

Relevant literature:

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

The following paper was also mentioned:

J. Milnor, On the concept of attractor. Commun.Math. Phys. 99 (1985), 177-195

 

Intro

 Ipad notes during lecture

Video available on  blackboard