Chaotic Expansive Homeomorphisms on Closed Orientable Surfaces of Positive Genus

Jiehua Mai; Song Shao

doi:10.1007/s40304-015-0061-2

Communications in Mathematics and Statistics ›› 2015, Vol. 3 ›› Issue (3) : 291 -314. DOI: 10.1007/s40304-015-0061-2

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Chaotic Expansive Homeomorphisms on Closed Orientable Surfaces of Positive Genus

Jiehua Mai ¹
, Song Shao ²^,^b

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Abstract

In this paper we give a new and elementary proof to the following fact: each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism. Further more, we show that the homeomorphisms given are also weakly mixing.

Keywords

Expansive homeomorphism / Chaotic homeomorphism / Closed orientable surface

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Jiehua Mai,Song Shao. Chaotic Expansive Homeomorphisms on Closed Orientable Surfaces of Positive Genus. Communications in Mathematics and Statistics, 2015, 3(3): 291-314 DOI:10.1007/s40304-015-0061-2