Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 905-912

LIPSCHITZ EQUIVALENCE OF SELF-SIMILAR SETS WITH EXACT OVERLAPS

Kan Jiang, Songjing Wang and Lifeng Xi

Ningbo University, Department of Mathematics
Ningbo 315211, P.R. China; jiangkan 'at' nbu.edu.cn

Ningbo University, Department of Mathematics
Ningbo 315211, P.R. China; wangsongjing 'at' nbu.edu.cn

Ningbo University, Department of Mathematics
Ningbo 315211, P.R. China; xilifeng 'at' nbu.edu.cn

Abstract. In this paper, we study a class A(λ,n,m) of self-similar sets with m exact overlaps generated by n similitudes of the same ratio λ. We obtain a necessary condition for a self-similar set in A(λ,n,m) to be Lipschitz equivalent to a self-similar set satisfying the strong separation condition, i.e., there exists an integer k ≥ 2 such that x^2k – mx^k + n is reducible, in particular, m belongs to {aⁱ : a ∈ N with i ≥ 2}.

2010 Mathematics Subject Classification: Primary 28A80.

Key words: Self-similar set, exact overlap, Lipschitz equivalence, strong separation condition.

Reference to this article: K. Jiang, S. Wang and L. Xi: Lipschitz equivalence of self-similar sets with exact overlaps. Ann. Acad. Sci. Fenn. Math. 43 (2018), 905-912.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4347