Stochastic stability in a model of drilling (Q1570901)

This paper deals with the stability of dynamics in the so-called one-dimensional model of drilling. This model was suggested by A. Lasota and P. Rusek and describes dynamical properties of the drilling process by the consideration of a piecewise monotonic transformation (say \(\beta)\) depending on scalar and functional parameters. The author tries to describe to what extent the abstract mode \(\beta\) is adequate for the behaviour of the real physical system. Here a small random perturbation of \(\beta\), modelling the fluctuations in the real system, is considered. It is shown that dynamical properties of the perturbed and the unperturbed models are almost the same.