About the Project

hyperelliptic

AdvancedHelp

(0.001 seconds)

4 matching pages

1: 22.19 Physical Applications
§22.19(iv) Tops
The classical rotation of rigid bodies in free space or about a fixed point may be described in terms of elliptic, or hyperelliptic, functions if the motion is integrable (Audin (1999, Chapter 1)). Hyperelliptic functions u ( z ) are solutions of the equation z = 0 u ( f ( x ) ) 1 / 2 d x , where f ( x ) is a polynomial of degree higher than 4. …A more abstract overview is Audin (1999, Chapters III and IV), and a complete discussion of analytical solutions in the elliptic and hyperelliptic cases appears in Golubev (1960, Chapters V and VII), the original hyperelliptic investigation being due to Kowalevski (1889). …
2: 31.8 Solutions via Quadratures
The variables λ and ν are two coordinates of the associated hyperelliptic (spectral) curve Γ : ν 2 = j = 1 2 g + 1 ( λ λ j ) . …
3: 21.7 Riemann Surfaces
§21.7(iii) Frobenius’ Identity
Let Γ be a hyperelliptic Riemann surface. …
4: 19.16 Definitions
with the same conditions on x , y , z as for (19.16.1), but now z 0 . … and R D is a degenerate case of R J , so is R J a degenerate case of the hyperelliptic integral, …