We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for
dynamical systems, as well as of the numerical techniques developed for the computation of …

We investigate the detailed dynamics of multi-dimensional Hamiltonian systems by studying
the evolution of volume elements formed by unit deviation vectors about their orbits. The …

We use the smaller alignment index (SALI) to distinguish rapidly and with certainty between
ordered and chaotic motion in Hamiltonian flows. This distinction is based on the different …

Chaotic nonlinear systems are systems whose main feature is extreme sensitivity to noise in
the problem or the corresponding initial conditions. In this paper, we examine the chaotic …

We present and compare different numerical schemes for the integration of the variational
equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the …

This book introduces and explores modern developments in the well established field of
Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the …

We provide a concise presentation of the Smaller (SALI) and the Generalized Alignment
Index (GALI) methods of chaos detection. These are efficient chaos indicators based on the …

The identification between chaos and ordered states in fractional-order chaotic systems is a
challenge as well as a hot topic due to the complex of fractional calculus. In this paper, the …

Abstract We apply the Mean Exponential Growth Factor of Nearby Orbits (MEGNO)
technique to the dynamics of Jovian irregular satellites. The MEGNO indicator is a practical …

The recently introduced GALI method is used for rapidly detecting chaos, determining the
dimensionality of regular motion and predicting slow diffusion in multi-dimensional …