O ct 1 99 4 BELAVKIN - KOLOKOLTSOVWATCH – DOG EFFECTS IN INTERAC - TIVELY CONTROLLED STOCHASTIC COMPUTER - GRAPHIC DY - NAMIC SYSTEMS

A pr 1 99 5 BELAVKIN - KOLOKOLTSOVWATCH – DOG EFFECTS IN INTERAC - TIVELY CONTROLLED STOCHASTIC COMPUTER - GRAPHIC DY - NAMIC SYSTEMS

Stochastic properties of the long time behavior of a continuously observed (and interactively controlled) quantum–field top are investigated mathematically. Applications to interactively controlled stochastic computer-graphic dynamic systems are discussed. 1 A preliminary shortened draft of this paper is located in the e–print archive of Los Alamos National Laboratories (USA) on Chaos and Dynam...

ha o - dy n / 99 10 02 0 v 1 1 4 O ct 1 99 9 A Stochastic Approach to the Construction of One - Dimensional Chaotic Maps with Prescribed Statistical Properties

We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power o...

ar X iv : c ha o - dy n / 99 10 00 5 v 1 6 O ct 1 99 9 The Finite - Difference Analysis and Time Flow

ar X iv : q ua nt - p h / 05 10 02 8 v 1 4 O ct 2 00 5 QUANTUM DIFFUSION , MEASUREMENT AND FILTERING

A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative stochastic analysis and integration are outlined. Algebraic differential equations that unify the quantum non Markovian diffusion with continuous non demolition ...

X iv : c ha o - dy n / 99 10 02 5 v 1 1 8 O ct 1 99 9 Asymptotic expansions of unstable ( stable ) manifolds in time - discrete systems

By means of an updated renormalization method, we construct asymptotic expansions for unstable manifolds of hyperbolic fixed points in the double-well map and the dissipative Hénon map, both of which exhibit the strong homoclinic chaos. In terms of the asymptotic expansion , a simple formulation is presented to give the first homoclinic point in the double-well map. Even a truncated expansion o...