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 {*a*^{i} :
*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

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