Strangely Dispersed Minimal Sets in the Quasiperiodically Forced Arnold Circle Map

Glendinning, Paul and Jager, Tobias and Stark, Jaroslav (2008) Strangely Dispersed Minimal Sets in the Quasiperiodically Forced Arnold Circle Map. [MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations
Depositing User: Professor Paul Glendinning
Date Deposited: 06 Nov 2008
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1178

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