| Abstract: |
| We investigate the accessible rotation numbers arising from parametrized Brown-Barge-Martin (BBM for short) embeddings of inverse limits of topological graphs as in [BCH13]. Among our results, we show the existence of homeomorphisms of $\mathbb{S}^2$ with Lakes of Wada rotational attractors, that are arbitrarily close to the identity. We also study accessible rotation numbers of BBM embedings of the reduced Arnold` Standard Family, which leads to a parametrised family of Birkhoff-like cofrontier attractors, where for uncountably many parameter values the two accessible rotation numbers are irrational. This complements the negative resolution of Walker`s Conjecture in [KLN15].
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References
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[BCH13] Boyland, P.; de Carvalho, A.; Hall, T.; Inverse limits as attractors in parameterized families. Bull. Lond. Math. Soc. 45:1075-1085, 2013
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[KLN15] Koropecki, A; Le Calvez, P.; Nassiri, M.; Prime ends rotation numbers and periodic points. Duke Math. J. 164:403-472, 2015 |
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