Journal
GEOMETRY & TOPOLOGY
Volume 22, Issue 4, Pages 2145-2186Publisher
GEOMETRY & TOPOLOGY PUBLICATIONS
DOI: 10.2140/gt.2018.22.2145
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We show that if f is an annular homeomorphism admitting an attractor which is an irreducible annular continua with two different rotation numbers, then the entropy of f is positive. Further, the entropy is shown to be associated to a C-0-robust rotational horseshoe. On the other hand, we construct examples of annular homeomorphisms with such attractors for which the rotation interval is uniformly large but the entropy approaches zero as much as desired. The developed techniques allow us to obtain similar results in the context of Birkhoff attractors.
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