Hamburg 2001 – scientific programme

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DY: Dynamik und Statistische Physik

DY 52: Nichtlineare Dynamik II

DY 52.3: Talk

Friday, March 30, 2001, 12:30–12:45, S 5.5

Flow Equations in Classical Mechanics — •Oliver Strebel — Handjerystr. 31, 12159 Berlin

The theory of flow equations developed by Wegner et. al. [1] for quantum mechanical systems is transfered to classical mechanics. In quantum mechanics flow equations are used to reduce the nondiagonal elements of Hamiltonian matrixes. Here it will be shown that using this technique an approximate separation of the Hamilton-Jacobi equation can be obtained.
A theory is presented, where flow equations are introduced as truncated Lie transforms of the coordinates and the nonintegrable Hamiltonian function yielding near-identity canonical transformations. The approximately separated equations are then integrated analytically.
As a nonintegrable example Chirikov’s model [2] is studied at primary resonance. The results are compared to analytical calculations using the method of averaging and to numerical experiments. This shows that flow equations are an interesting alternative for perturbative calculations in classical mechanics.

[1] F. Wegner; Ann. Phys. (Leipzig) 3, p.77 (1994).
[2] A.J. Lichtenberg, M.A. Lieberman; Regular and Chaotic Dynamics 2nd ed.; Springer AMS 38, p.395 (1992).