Strong stochastic stability and rate of mixing for unimodal maps

Strong stochastic stability and rate of mixing for unimodal maps

We consider small random perturbations of a large class of nonuniformly hy-perbolic unimodal maps and prove stochastic stability in the strong sense (L 1-convergence of invariant densities) and uniform bounds for the exponential rate of decay of correlations. Our method is based on an analysis of the spectrum of a modiied Perron-Frobenius operator for a tower extension of the Markov chain.

Almost Sure Rates of Mixing for I.i.d. Unimodal Maps

simulation and experimental studies for prediction mineral scale formation in oil field during mixing of injection and formation water

abstract: mineral scaling in oil and gas production equipment is one of the most important problem that occurs while water injection and it has been recognized to be a major operational problem. the incompatibility between injected and formation waters may result in inorganic scale precipitation in the equipment and reservoir and then reduction of oil production rate and water injection rate. ...

Bifurcations of Unimodal Maps

We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) renormalization approach to the study of the statistical properties of typical unimodal maps.

Chaotic Unimodal and Bimodal Maps

We describe up to conjugacy all unimodal and bimodal maps that are chaotic, by giving necessary and sufficient conditions for unimodal and bimodal maps of slopes ±s to be transitive.