Strong coincidence and overlap coincidence

Shigeki Akiyama

doi:10.3934/dcds.2016027

Article Contents

2016, Volume 36, Issue 10: 5223-5230. Doi: 10.3934/dcds.2016027

This issue Previous Article Next Article Positive solutions to indefinite Neumann problems when the weight has positive average

Strong coincidence and overlap coincidence

Shigeki Akiyama^1,

1.
Institute of Mathematics, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 350-8571

Received: September 2015

Revised: December 2015

Published: May 2017

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Abstract

We show that strong coincidences of a certain many choices of control points are equivalent to overlap coincidence for the suspension tiling of Pisot substitution. The result is valid for dimension $\ge 2$ as well, under certain topological conditions. This result gives a converse of the paper [2] and elucidates the tight relationship between two coincidences.

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Mathematics Subject Classification: Primary: 52C23; Secondary: 37B50, 11K16.

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