  In this work, noise is used to analyze the penetration of regular islands in
conservative dynamical systems. For this purpose we use the standard map
choosing nonlinearity parameters for which a mixed phase space is present. The
random variable which simulates noise assumes three distributions, namely
equally distributed, normal or Gaussian, and power-law (obtained from the same
standard map but for other parameters). To investigate the penetration process
and explore distinct dynamical behaviors which may occur, we use recurrence
time statistics (RTS), Lyapunov exponents (LEs) and the occupation rate of the
phase space. Our main findings are as follows: (i) the standard deviations of
the distributions are the most relevant quantity to induce the penetration;
(ii) the penetration of islands induce power-law decays in the RTS as a
consequence of enhanced trapping; (iii) for the power-law correlated noise an
algebraic decay of the RTS is observed, even though sticky motion is absent;
and (iv) although strong noise intensities induce an ergodic-like behavior with
exponential decays of RTS, the largest Lyapunov exponent is reminiscent of the
regular islands.
