Periodic functions: self-intersection and local singular points. (English) Zbl 07913028
Summary: Self-intersections and local singular points of the curves play an important role in algebraic geometry and many other areas. In the present paper, we study the self-intersection and local singular points of the \(n\)-member chains. For this purpose, we derive and use several new results on trigonometric formulas. A unified approach for calculating self-intersection and local singular points for a wide class of curves is presented. An application to the spectral theory of integro-differential operators with difference kernels is given as well.
MSC:
| 14H20 | Singularities of curves, local rings |
| 14H50 | Plane and space curves |
| 33B10 | Exponential and trigonometric functions |
Keywords:
\(n\)-member chain; self-intersection point; singular point; rotating group; periodic helixReferences:
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