Polynomial Stochastic Dynamical Indicators

This paper introduces three types of dynamical indicators that capturethe effect of uncertainty on the time evolution of dynamical systems. Two indica-tors are derived from the definition of Finite Time Lyapunov Exponents while athird indicator directly exploits the property of the polynomial expansion of thedynamics with respect to the uncertain quantities. The paper presents the deriva-tion of the indicators and a number of numerical experiments that illustrates theuse of these indicators to depict a cartography of the phase space under paramet-ric uncertainty and to identify robust initial conditions and regions of practicalstability in the restricted three-body problem.