Unbounded regime for circle maps with a flat interval

Liviana Palmisano

doi:10.3934/dcds.2015.35.2099

Article Contents

2015, Volume 35, Issue 5: 2099-2122. Doi: 10.3934/dcds.2015.35.2099

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Unbounded regime for circle maps with a flat interval

Liviana Palmisano^1,

1.
Institute of Mathematics of PAN, ul. Śniadeckich 8, 00-956 Warszawa

Received: April 30, 2014

Revised: September 30, 2014

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 37E10.

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