Nonlinear science abstracts 277

336 (P3,T9) THE LONG-TIME BEHAVIOR OF A GENERALIZED LANGEVIN DYNAMICS AND ITS FLUCTUATION-DISSIPATION THEOREM, lwao Hosokawa, Department of Mechanical Engineering, lwate University, Morioka 020, JAPAN.

The long-time behavior or ultimate stationary state of a generalized Langevin dynamics with a linear memory kernel is investigated by the Fourier series method and using spectral representation of a general Gaussian noise. It turns out that the effect of an initial condition on the stochastic state vanishes in the transient time, which depends on the structure of the memory kernel function, and eventually it goes into an ultimate, Guasian stationary process, characterized by a general form of the fluctuation-dlssipation theorem.

JOURNAL: Submitted to Journal of Statistical Physics

337 (M4,T2) PARAMETRIC MODULATION OF INSTABILITIES OF A NONLINEAR DISCRETE SYSTEM, M. L~cke and Y. Saito, Institut f~r FestkDrperforschung der Kernforschunganslage 161ich, Postfach 1913, D-5170 161ich, WEST GERMANY.

The effect of modulation on the first instability of the logistic map is determined. Similarities with the response of a modulated,damped, anharmonic oscillator are discussed. We also discuss small-amplltude modulation of the period doubling bifurcations in the discrete system.

JOURNAL: unknown

338 (MI,T6) LYAPUNOV FUNCTIONS OF TWO VARIABLES AND A CONJUGACY THEOREM FOR DYNAMICAL SYSTEMS, by J. Lewowicz, E. Lima de S~ and J. Tolesa, Dep. de Matem~ticas, Universidad Sim6n Bolivar, Apartado 80659, Caracas 1080-A, VENEZUELA

A global conjugacy theorem concerning special perturbations of hyperbolic systems is proved, from which Hartman's classical local conjugacy result follows. The proof makes essential use of Lyapunov functions of two variables. In the last section a generalization of these results to nonlinear quasi-hyperbolic systems is briefly indicated

JOURNAL: Acta Cientlfica Venezolana

339 (P8,T9) A LANGEVlN APPROACH TO FERMION AND QUANTUM SPIN CORRELATION FUNCTIONS, John R. Klauder, Bell Laboratories, Murray Hill, NJ 07974 USA

By using spin-coherent states, we show that correlation functions for fermions or quantum spins follow from solutions to Langevin equations associated with a functional integral representation of the partition function. Our method is applicable to any number of dimensions, may also be combined with boson variables, and is suitable for computer simulations.

JOURNAL: unknown

340 (PIO,T9)REMARKS ON A STOCHASTIC QUANTIZATION OF SCALAR FIELDS, John R. Klauder, Bell Laboratories, Murray Hill, NJ 07974, USA; Hiroshi Ezawa, Department of Physics, Gakushuln Universlty, Toshima-ku, Tokyo 171, JAPAN.

The Langevin equation approach to derive (non)equilibrium- distribution correlation functions for scalar fields is examined. Regularization introduced by the auxiliary time renders the parameters of the Langevin equation finite in the case of super renormalizable models while causing no change in the boundary between renormalizability and nonrenormalizability. An heuristic central-limit-type argument is suggested to understand the free-field behavior of

(~4) n models, n > 4. renormalizable JOURNAL : unknown