Random Dynamical Systems

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Normal Forms for Nonautonomous Differential Equations (2002, neutral): “Arnold [2] for random dynamical systems.”
Hausdorff dimension of planar self-affine sets and measures (2017, background): “ectionontothe1 dimensionalsubspacecontaining x 1 . Hence,wecandeﬁnealinearmap!u(i ) : I7!R as !u(i ;x) = xsl(i i) + tr(i ): Deﬁnition7.7. Wesaythat!u isatransversalfamily,ifforany i 6= j thereexistsx2[0;1] suchthat!u(i ;x) = !u(j ;x) thensl(i ) 6= sl(j ). Proposition7.8. LetFbeasin (7.2). Supposetha”
Comparison of various concepts of a random attractor:¶ A case study (2002, background): “While the concept of an attractor for deterministic dynamical systems is well-established, the same can not be said for random dynamical systems, which have gained considerable attention during the past decade (for a comprehensive survey see [1]).”
Dynamical Systems and Linear Algebra (2014, background): “The general situation is discussed in [BK94], the case of linearization at a periodic solution is covered in [Rob98], random dynamical systems are treated in [Arn98], and robust systems (control systems) are the topic of [CK00].”
Sample path properties of the stochastic flows (2001, background): “The measure At has been extensively studied and part (b) is well known, see Arnold (1998). Dimensional characteristics of It have been studied in several papers [Ledrappier and Young (1988a, b) and Le Jan (1985, 1986a, b)].”