Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space

By Zeng Lian, Kening Lu. 2010

170 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/60af798243e873be3c509a5db936791aac693492

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Invariant Manifolds for Random and Stochastic Partial Differential Equations (2009, background): “When a multiplicative ergodic theorem (MET) holds [21, 18], nonuniform pseudo-hyperbolicity also holds.”
A concise proof of the Multiplicative Ergodic Theorem on Banach spaces (2014, background): “Recently, Lian and Lu [6] proved a version in the context of linear operators on separable Banach spaces, in which the continuity assumption was relaxed to a measurability condition.”
A volume-based approach to the multiplicative ergodic theorem on Banach spaces (2015, background): “Doan, in his PhD thesis [11], carried out an analogous deduction for strongly measurable cocycles on a separable Banach space, assuming the MET in [10].”
A semi-invertible operator Oseledets theorem (2011, methodology): “The following theorem was obtained by Doan [13] as a corollary of the two-sided Oseledets theorem proved by Lian and Lu [34].”
Local Entropy Theory of a Random Dynamical System (2011, background): “st studied in the framework of the relativized ergodic theory of Ledrappier and Walters [48] and later in the theory of random local entropy theory of a random dynamical system 3 transformations, see [2, 8, 9, 10, 15, 41, 43, 44, 45, 46, 49, 52, 53, 54]. In particular, it was shown in [8] that the A”
Lyapunov Exponents, Periodic Orbits and Horseshoes for Mappings of Hilbert Spaces (2011, methodology): “with regard to the asymptotic properties of Df x , generalizations of Oseledets’ Multiplicative Ergodic Theorem [11] to cocycles of linear maps of Hilbert and Banach spaces have been known for some time: a version of this result for compact operators of Hilbert spaces was proved in [15]; Banach spac”
Lyapunov exponents, periodic orbits, and horseshoes for semiflows on Hilbert spaces (2012, background): “…of the tangent space H x at x into (some of these factors may be trivial) with the following properties: which follows immediately from (C3)(iii), ( F, μ ) and the discrete-time system ( f, μ ) deﬁned by its time-1 map have the same Lyapunov exponents and associated sub-spaces; see e.g. [5].”
A semi-invertible Oseledets Theorem with applications to transfer operator cocycles (2010, methodology): “The cost (which is again heavy from the point of view of applications) is that in order to obtain suitable measurability Lian imposes the condition that the Banach space X be separable.”