Final state sensitivity in noisy chaotic scattering

TL;DR

This paper investigates how noise influences unpredictability in chaotic scattering, introducing probabilistic tools like probability basins and noise-sensitivity exponents to quantify and analyze the effects.

Contribution

It develops new probabilistic concepts and methods to analyze the impact of noise on unpredictability in chaotic scattering systems.

Findings

Noise increases unpredictability in chaotic scattering.

Probability basins and noise-sensitivity exponents effectively quantify noise effects.

Unpredictability cannot be fully understood by traditional nonlinear dynamics methods.

Abstract

The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the dynamical behavior and it models their internal irregularities or their coupling with the environment. In these situations the unpredictability is affected by both the chaotic dynamics and the stochastic fluctuations. In the presence of noise two trajectories with the same initial condition can evolve in different ways and converge to a different asymptotic behavior. For this reason, even the exact knowledge of the initial conditions does not necessarily lead to the predictability of the final state of the system. Hence, the noise can be considered as an important source of unpredictability that cannot be fully understood using the conventional methods of nonlinear dynamics, such as the exit basins and the uncertainty exponent. By adopting a probabilistic point of view, we develop the concepts of probability basin, uncertainty basin and noise-sensitivity exponent, that allow us to carry out both a quantitative and qualitative analysis of the unpredictability on noisy chaotic scattering problems.