The Fast Norm Vector Indicator (FNVI) method: A new dynamical parameter for detecting order and chaos in Hamiltonian systems

Abstract

In the present article, we introduce and also deploy a new, simple, very fast and efficient method, the Fast Norm Vector Indicator (FNVI) in order to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian systems. This distinction is based on the different behavior of the FNVI for the two cases: the indicator after a very short transient period of fluctuation displays a nearly constant value for regular orbits, while it continues to fluctuate significantly for chaotic orbits. In order to quantify the results obtained by the FNVI method, we establish the dFNVI, which is the quantified numerical version of the FNVI. A thorough study of the method's ability to achieve an early and clear detection of an orbit's behavior is presented both in two and three degrees of freedom (2D and 3D) Hamiltonians. Exploiting the advantages of the dFNVI method, we demonstrate how one can rapidly identify even tiny regions of order or chaos in the phase space of Hamiltonian systems. The new method can also be applied in order to follow the time evolution of sticky orbits. A detailed comparison between the new FNVI method and some other well-known dynamical methods of chaos detection reveals the great efficiency and the leading role of this new dynamical indicator.

Published in Nonlinear Dynamics (NODY) journal. The structure of the article was formatted following arXiv:nlin/0404058 as a guide. arXiv admin note: previous paper with related context: arXiv:nlin/0404058; text overlap with arXiv:0704.3155 by other authors

References in corpus (3)

• A new dynamical model for the study of galactic structure
• Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits
• Application of new dynamical spectra of orbits in Hamiltonian systems

Cited by in corpus (8)

• Visualization and comparison of classical structures and quantum states of 4D maps
• A Hamiltonian system of three degrees of freedom with eight channels of escape: The Great Escape
• Escapes in Hamiltonian systems with multiple exit channels: Part I
• Revealing the evolution, the stability and the escapes of families of resonant periodic orbits in Hamiltonian systems
• Escapes in Hamiltonian systems with multiple exit channels: Part II
• Order and chaos in a new 3D dynamical model describing motion in non axially symmetric galaxies
• Determining the nature of orbits in disk galaxies with non spherical nuclei
• Exploring the origin, the nature and the dynamical behaviour of distant stars in galaxy models