Complex/Dynamical Systems Seminar - Hector LomelÃ
| Event Description: Hector LomelÃ, , ON HAMILTONIAN FLOWS WHOSE ORBITS ARE STRAIGHT LINESÌý Ìý We say that a Hamiltonian $H$ is affine-integrable if itsÌý flow is linear in time. Trivial examples are Hamiltonians $H(q; p)$ that do not depend on the coordinate $q$. By a theorem of Moser, every polynomial Hamiltonian of degree 3 reduces to such a $q$-independent Hamiltonian via a linear symplectic change of variables. We show that such a reduction is impossible, in general, for polynomials of degree 4 or higher. But we give a condition that implies linear-symplectic conjugacy to another simple class of Hamiltonians. The condition is shown to hold for all nondegenerate Hamiltonians that are homogeneous of degree 4. Ìý The time-1 maps of affice-integrable flows appear in numerical analysis and physics,Ìý They are known as jolt-maps and constitute the basic building blocks in the so-called Dragt-Finn factorization of more general symplectic maps. This factorization has proved to be Ìýuseful in symplectic numerical schemes, including the simulation of Hamiltonian of flows in plasmas. Ìý (Joint work with Hans Koch.) Ìý |
| Location Information: ÌýÌý() 1111 Engineering DR Â鶹ӰԺ, CO Room:Ìý226: Applied Math Conference Room |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 Email: amassist@colorado.edu |