We define a modified version of Erschler and Karlsson construction of homomorphisms from random walks [A. Erschler and A. Karlsson, Ann. Inst. Fourier (Grenoble) 60 (2010), no. 6, 2095−2113]. We show that our definition is well adapted to semidirect products. The same construction is conjectured to work also for other classes of maps like quasi-morphisms.
Bettencourt, Gast?o and Mendes, Sérgio
"Homomorphism to R of Semidirect Products: A Dynamical Construction,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 22.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss5/22