Chun-Yun Cao

Finite pattern problems in infinite iterated function systems

Let { f n } n ≥ 1 be an infinite iterated function system on [ 0 , 1 ] and let Λ be its attractor. Then, any x ∈ Λ corresponds to a sequence of integers { a n ( x ) } n ≥ 1 , called the digit sequence of x , in the sense that x = lim n → ∞ ⁡ f a 1 ( x ) ∘ ⋯ ∘ f a n ( x ) ( 1 ) ....