Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying 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 plethora of methods for chaos detection and predictability.
The most commonly employed technique for investigating chaotic dynamics i.e. the computation
of Lyapunov exponents however may suffer a number of problems and drawbacks for example when
applied to noisy experimental data. In the last two decades several novel methods have been
developed for the fast and reliable determination of the regular or chaotic nature of orbits
aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes
and tutorial reviews serves as an introduction to and overview of modern chaos detection and
predictability techniquesfor graduate students and non-specialists. The book covers theoretical
and computational aspects of traditional methods to calculate Lyapunov exponents as well as of
modern techniques like the Fast (FLI) the Orthogonal (OFLI) and the Relative (RLI) Lyapunov
Indicators the Mean Exponential Growth factor of Nearby Orbits (MEGNO) the Smaller (SALI) and
the Generalized (GALI) Alignment Index and the '0-1' test for chaos.
