Complex/Dynamical Systems Seminar - Sebasti谩n Ferrer
| Event Description: , , , Spain On the N-Extended Euler System. Generalized Jacobi Elliptic Functions We study the integrable system 蝇i(蠀)痛 = 伪i 鈭 蝇j(蠀), 听 听 听 听 听 听听 伪2鈭堚劃,听听听听听听听听听听听听 (1鈮 i; j 鈮 N) 听听听听听听听听听听听听听听听听听 j鈮爄 of first order differential equations as a initial value problem 蝇i(0)鈭堚劃. The analysis is based on its quadratic first integrals Cij = 伪i 蝇j(蠀)2 - 伪j 蝇i(蠀)2. When N = 3 this system generalizes the classic Euler system for the rigid body, thus we call it N-extended Euler system. Denoting 蝇 = (蝇1, 鈥 , 蝇N), the function 惟(蠀) = 鈨τ 鈨2 generalizes the Weierstrass elliptic function. For each dimension N 鈮 5 the system defines a family of functions, generically hyperelliptic functions. In this presentation we focus on the cases N = 4 and N = 5. Taking into account its nested structure of the system, we propose parametrizations 蠀 鈫 蠀*: d蠀 = g(蝇i) d蠀 that separates each trajectory from its time equation.The main result is the generalization of the Jacobi elliptic functions. Other aspects such as the geometric properties of the N-system or the numeric computation of the functions involved, are also in progress. |
| Location Information: 听听() 1111 Engineering DR 麻豆影院, CO Room:听226: Applied Math Conference Room |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |