Hokkaido Mathematical Journal

BI\'S Andrzej, NAKAYAMA Hiromichi, WALCZAK Pawe\l,

Modeling minimal foliated spaces with positive entropy.

Hokkaido Mathematical Journal, 36 (2007) pp.283-310

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Abstract

Using methods and results of decomposition theory we construct minimal actions of groups of homeomorphisms of some classical fractals (the Sierpi\'nski carpet and its generalizations, and the Menger curve) with positive entropy. Suspending these group actions we get minimal foliated spaces which have positive geometric entropy and are modelled on these fractals.

MSC(Primary)37C85
MSC(Secondary)57R30
Uncontrolled Keywordsgroup action, Sierpi\'nski sets, foliation