Complex/Dynamical Systems Seminar - Sebastián Ferrer
| Event Description: , , , Spain On the N-Extended Euler System. Generalized Jacobi Elliptic Functions We study the integrable system Ӭi(υ)ʹ = αi ∏ Ӭj(υ), α2∈ℝ, (1≤ i; j ≤ N) j≠i of first order differential equations as a initial value problem Ӭi(0)∈ℝ. The analysis is based on its quadratic first integrals Cij = αi Ӭj(υ)2 - αj Ӭi(υ)2. When N = 3 this system generalizes the classic Euler system for the rigid body, thus we call it N-extended Euler system. Denoting Ӭ = (Ӭ1, … , ӬN), the function Ω(υ) = ⃦Ӭ ⃦2 generalizes the Weierstrass elliptic function. For each dimension N ≥ 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 υ → υ*: dυ = g(Ӭi) dυ 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: () 1111 Engineering DR Boulder, CO Room:226: Applied Math Conference Room |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |