Chaos Detection and Predictability

This set of lectures notes and tutorial reviews, edited and authored by some of the pioneers of the novel methods described, is meant to be a textbook-like introduction and review of modern chaos detection and predictability methods, both theoretical and computational, for graduate students and non-specialists.

 Being able to distinguish chaoticity from regularity in deterministic dynamical systems and to be able to determine the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a priori a plethora of methods for chaos detection, phase space reconstruction and predictability, yet some of most commonly employed techniques for investigating chaotic dynamics, e.g. the computation of Lyapunov Exponents, suffer an number of problems and drawbacks in certain situations.

 In the last two decades, several novel methods – at the core of the present volume - have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, which were aimed at overcoming the shortcomings of more traditional such as the fast and relative Lyapunov indicators, the smaller alignment index and the generalized alignment index, the mean exponential growth of nearby orbits, the frequency map analysis and the so-called ‘0-1’ test.