Cross-ratio inequality with infinite type of singularities. (English) Zbl 1370.37081
Summary: Let \(f\) be a preserving orientation circle homeomorphism with infinite number of break points, i.e., the points at which the derivative of \(f\) has jumps, and finite number of singular points, i.e., the points \(x_{i}\), \(i=1,2,\dots,n\), such that \(f'(x_{i})=\infty\), \(i=1,2,\dots,n\). Then the cross-ratio inequality with respect to \(f\) holds.
MSC:
| 37E10 | Dynamical systems involving maps of the circle |
| 37C15 | Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems |
| 37E45 | Rotation numbers and vectors |
References:
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