Quenched stochastic stability for eventually expanding-on-average random interval map cocycles

@article{Froyland2019QuenchedSS,
  title={Quenched stochastic stability for eventually expanding-on-average random interval map cocycles},
  author={Gary Froyland and Cecilia Gonz{\'a}lez-Tokman and Rua Murray},
  journal={Ergodic Theory and Dynamical Systems},
  year={2019},
  volume={39},
  pages={2769 - 2792}
}
The paper by Froyland, González-Tokman and Quas [Stability and approximation of random invariant densities for Lasota–Yorke map cocycles. Nonlinearity 27(4) (2014), 647] established fibrewise stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota–Yorke maps under a variety of perturbations, including ‘Ulam’s method’, a popular numerical method for approximating acims. The expansivity requirements of Froyland et al were that the cocycle (or powers of… 

References

SHOWING 1-10 OF 54 REFERENCES
Stability and approximation of random invariant densities for Lasota-Yorke map cocycles
We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be
Ulam's method for some non-uniformly expanding maps
Certain dynamical systems on the interval with indifferent fixed points admit invariant probability measures which are absolutely continuous with respect to Lebesgue measure. These maps are often
Exponential Decay of Correlations for Random Lasota–Yorke Maps
Abstract:We consider random piecewise smooth, piecewise invertible maps mainly on the interval but also in higher dimensions. We assume that, on the average and possibly without any stochastic
Ulam's Method for Lasota-Yorke Maps with Holes
TLDR
It is proved that a simple adaptation of the standard Ulam scheme provides convergent sequences of escape rates, conditional invariant densities, and quasi-conformal measures from the corresponding right eigenvector for Lasota-Yorke maps with holes.
Absolutely Continuous S.R.B. Measures For Random Lasota-Yorke Maps
A. Lasota and J. A. Yorke 19] proved that a piecewise expanding interval map admits nitely many ergodic absolutely continuous invariant probability measures. We generalize this to the random
Ulam's method for random interval maps
TLDR
This work extends Ulam's construction to the situation where a family of piecewise monotonic transformations are composed according to either an iid or Markov law, and proves an analogous convergence result.
Random perturbations of nonuniformly expanding maps
— We give both sufficient conditions and necessary conditions for the stochastic stability of nonuniformly expanding maps either with or without critical sets. We also show that the number of
Stochastic stability versus localization in one-dimensional chaotic dynamical systems
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this
Asymptotic Behaviors of Dynamical Systems with Random Parameters
In this paper we will investigate asymptotic behaviors of random orbits of dynamical systems with random parameters. In many biological models (for example, May's model [13]), the dynamical systems
...
...