# Characterization of SRB Measures for Random Dynamical Systems on Banach space

@inproceedings{Luo2022CharacterizationOS, title={Characterization of SRB Measures for Random Dynamical Systems on Banach space}, author={Chiyi Luo and Yun Zhao}, year={2022} }

. This paper considers C 2 random dynamical systems on a Banach space, and proves that under some mild conditions, SRB measures are char- acterized by invariant measures satisfying the Pesin entropy formula, in which entropy is equal to the sum of positive Lyapunov exponents of the system. This result is a random version of the main result in A. Blumenthal and L.-S. Young’s paper [12].

## References

SHOWING 1-10 OF 41 REFERENCES

### Characterization of Measures Satisfying the Pesin Entropy Formula for Random Dynamical Systems

- Mathematics
- 1998

In this paper we first give a formulation of SRB (Sinai–Ruelle–Bowen) property for invariant measures of “stationary” random dynamical systems and then prove that this property is sufficient and…

### The metric entropy of random dynamical systems in a Banach space: Ruelle inequality

- MathematicsErgodic Theory and Dynamical Systems
- 2012

Abstract Consider a random cocycle Φ on a separable infinite-dimensional Banach space preserving a probability measure, which is supported on a random compact set. We show that if Φ satisfies some…

### Existence of SRB Measures for A Class of Partially Hyperbolic Attractors in Banach spaces

- Mathematics
- 2016

In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial…

### The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropyformula

- Mathematics
- 2013

Consider a random cocycle $\Phi$ on a separable
infinite-dimensional Hilbert space preserving a probability measure
$\mu$, which is supported on a random compact set $K$. We show that
if $\Phi$ is…

### Entropy, volume growth and SRB measures for Banach space mappings

- Mathematics
- 2015

We consider $$C^2$$C2 Fréchet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a…

### Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles

- MathematicsAnnales Academiae Scientiarum Fennicae Mathematica
- 2019

We prove that for semi-invertible and H\"older continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all…

### Lyapunov Exponents, Periodic Orbits and Horseshoes for Mappings of Hilbert Spaces

- Mathematics
- 2011

We consider smooth (not necessarily invertible) maps of Hilbert spaces preserving ergodic Borel probability measures, and prove the existence of hyperbolic periodic orbits and horseshoes in the…

### Oseledets Splitting and Invariant Manifolds on Fields of Banach Spaces

- MathematicsJournal of Dynamics and Differential Equations
- 2019

We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an application, we prove…