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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
A topological proof of the Arnold four cusps theorem
V. A. Vassilievab a Steklov Mathematical Institute, 8 Gubkina str., Moscow 119991, Russia
b Higher School of Economics
Аннотация:
The Arnold theorem (generalizing a consideration by Jacobi) states that on a generic Riemannian surface, which is sufficiently close to a sphere, the kth caustic of a generic point has at least four semi-cubical vertices. We prove this fact by the methods of the Morse theory; in particular, we replace the previous analytical condition of the ‘sufficient closeness to the sphere’ by a geometric one, which probably is considerably less restrictive.
Поступила в редакцию: 08.06.2011
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