Tree-like curve

A tree-like curve with finitely many marked double points

In mathematics, particularly in differential geometry, a tree-like curve is a generic immersion $c:S^{1}\to \mathbb {R} ^{2}$ with the property that removing any double point splits the curve into exactly two disjoint connected components. This property gives these curves a tree-like structure, hence their name. They were first systematically studied by Russian mathematicians Boris Shapiro and Vladimir Arnold in the 1990s.

See also

• Arnold invariants
• Gauss diagram
• Inflection point