Wandering domains of skew products and distribution of linear recurrent sequences mod 1 (Zhangchi CHEN - East China Normal University)

The existence of wandering domains is an interesting research topic in
higher-dimensional complex dynamics.
Let f=(p(z),q(z,w)) be a polynomial skew product map. Astorg and Boc Thaler
defined α,β (with α>1), two real invariants by the coefficients of f. They
prove that a sufficient number theoretical condition on (α,β) that f admits
wandering domains. They essentially asked this question: do we have other
pairs of (α,β) producing wandering domains?
In collaboration with Zihao Ye and Weizhe Zheng, we answered their question in
the case α is an algebraic number, using number theory and distribution of
linear recurrent sequences mod 1.
As an application in complex dynamical systems, we constructed new polynomial
skew product maps with wandering domains.