In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them.

Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy­ namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random ...

2006年8月7日 · The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems.

2006年10月20日 · Symbolic dynamics for expanding random dynamical systems. Random & Computational Dynamics , 1:219–227, 1992. MathSciNet MATH Google Scholar

The concept of random dynamical system is a com-paratively recent development combining ideas and methods from the well developed areas of probabil-ity theory and dynamical systems. Let us consider a mathematical model of some physi-cal process given by the iterates Tk 0 =T0 k ··· T0,k≥ 1, of a smooth transformation T0: M of a man-ifold ...

Random Dynamical Systems. V. Araújo, in Encyclopedia of Mathematical Physics, 2006. Introduction. The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well-developed …

2022年11月22日 · In the exercises, Bernoulli convolutions and the Propp-Wilson algorithm are explored. Whether it is on countable or non-countable state spaces, numerous examples of Markov chains are given by random dynamical systems (also called random iterative systems).

His paradigm of a random dynamical system (RDS for short) is based on an ultimately simple idea: view an RDS as consisting of two ingredients, a stochastic but autonomous “noise process,” and a classical dynamical system that is driven by this process. The noise process is described by a measure-preserving dynamical system.

2019年3月22日 · We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems.

Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.