Unbounded regime for circle maps with a flat interval
Liviana Palmisano
Discrete & Continuous Dynamical Systems - A 2015, 35(5): 2099-2122 doi: 10.3934/dcds.2015.35.2099
We study $\mathcal{C}^2$ weakly order preserving circle maps with a flat interval. In particular we are interested in the geometry of the mapping near to the singularities at the boundary of the flat interval. Without any assumption on the rotation number we show that the geometry is degenerate when the degree of the singularities is less than or equal to two and becomes bounded when the degree goes to three. As an example of application, the result is applied to study Cherry flows.
keywords: topological transitivity Cherry flows. circle mappings Low-dimensional dynamics non-wandering set

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