A Note on Double Minimality

Wen Huang; Xiangdong Ye

doi:10.1007/s40304-015-0051-4

Communications in Mathematics and Statistics ›› 2015, Vol. 3 ›› Issue (1) : 57 -61. DOI: 10.1007/s40304-015-0051-4

Article

A Note on Double Minimality

Wen Huang ¹
, Xiangdong Ye ¹^,^b

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Abstract

It is known that a minimal prime system is either a subshift or with a connected phase space (Keynes and Newton Trans Am Math Soc 217:237–255, 1976). We show that a double minimal system is a subshift; this implies immediately that no non-periodic map has 4-fold topological minimal self-joinings. We also prove that a POD system is either uniformly rigid or is a subshift.