Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits

By P. Cincotta, C. Giordano, Carles Simó. 2003

270 citations recorded by the source corpus.

In this paper we deal with an alternative technique to study global dynamics in Hamiltonian systems, the mean exponential growth factor of nearby orbits (MEGNO), that proves to be efficient to investigate both regular and stochastic components of phase space. It provides a clear picture of resonance structures, location of stable and unstable periodic orbits as well as a measure of hyperbolicity in chaotic domains which coincides with that given by the Lyapunov characteristic number. Here the MEGNO is applied to a rather simple model, the 3D perturbed quartic oscillator, in order to visualize the structure of its phase space and obtain a quite clear picture of its resonance structure. Examples of application to multi-dimensional canonical maps are also included.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8c807efdfdea4922ecf5ac0170945db0d2c163a1

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In Computer Networks and Communications

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

WHFAST: a fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long-term gravitational simulations (2015, background): “A more recent approach with similar informative value is the Mean Exponential Growth factor of Nearby Orbits, or MEGNO for short (Cincotta et al. 2003).”
The Lyapunov Characteristic Exponents and Their Computation (2008, methodology): “Among other chaoticity detectors, belonging to the same category with the evaluation of the mLCE, are the fast Lyapunov indicator (FLI) [58, 59, 56, 89, 49, 69] and its variants [4, 5], the smaller alignment index (SALI) [122, 124, 125] and its generalization, the so-called generalized alignment ind”
On the Implementation of the 0-1 Test for Chaos (2009, background): “Much progress has been made in developing tests for chaos [13, 14, 25, 7, 2 , 1]. Recently we have introduced a binary test for chaos, the 0–1 test, designed for the analysis of deterministic dynamical systems [8, 9]. The test distinguishes between regular and chaotic dynamics for a deterministic s”
Kepler Planet Masses and Eccentricities from TTV Analysis (2016, unknown): “Sanchis-Ojeda et al. (2012) fit masses m m, 11.3 1.4,b c = [ ] [ 10 We confirm the chaotic nature of the initial conditions that produce alternating evolution with the MEGNO chaos indicator (Cincotta et al. 2003) implemented in the REBOUND code.”