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2008.101: Strangely Dispersed Minimal Sets in the Quasiperiodically Forced Arnold Circle Map

2008.101: Paul Glendinning, Tobias Jager and Jaroslav Stark (2008) Strangely Dispersed Minimal Sets in the Quasiperiodically Forced Arnold Circle Map.

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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.

Item Type:MIMS Preprint
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 39 Difference and functional equations
MIMS number:2008.101
Deposited By:Professor Paul Glendinning
Deposited On:06 November 2008

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