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arXiv · 0807.4707

Strangely dispersed minimal sets in the quasiperiodically forced Arnold map

P. Glendinning·T. Jaeger·J. Stark
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Abstract

We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely dispersed'. Along the way, we generalise some well-known results about circle endomorphisms to the uniquely ergodically forced case. Namely, all rotation numbers in the rotation interval of a uniquely ergodically forced circle endomorphism are realised on minimal sets, and if the rotation interval has non-empty interior then the topological entropy is strictly positive. The results apply in particular to the quasiperiodically forced Arnold circle map, which serves as a paradigm example.

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P. Glendinning, T. Jaeger, J. Stark. 2008-07-29. Strangely dispersed minimal sets in the quasiperiodically forced Arnold map. https://doi.org/10.1088/0951-7715%2F22%2F4%2F008

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