Application of new dynamical spectra of orbits in Hamiltonian systems

Abstract

In the present article, we investigate the properties of motion in Hamiltonian systems of two and three degrees of freedom, using the distribution of the values of two new dynamical parameters. The distribution functions of the new parameters, define the S(g) and the S(w) dynamical spectra. The first spectrum definition, that is the S(g) spectrum, will be applied in a Hamiltonian system of two degrees of freedom (2D), while the S(w) dynamical spectrum will be deployed in a Hamiltonian system of three degrees of freedom (3D). Both Hamiltonian systems, describe a very interesting dynamical system which displays a large variety of resonant orbits, different chaotic components and also several sticky regions. We test and prove the efficiency and the reliability of these new dynamical spectra, in detecting tiny ordered domains embedded in the chaotic sea, corresponding to complicated resonant orbits of higher multiplicity. The results of our extensive numerical calculations, suggest that both dynamical spectra are fast and reliable discriminants between different types of orbits in Hamiltonian systems, while requiring very short computation time in order to provide solid and conclusive evidence regarding the nature of an orbit. Furthermore, we establish numerical criteria in order to quantify the results obtained from our new dynamical spectra. A comparison to other previously used dynamical indicators, reveals the leading role of the new spectra.

arXiv commentPublished in Nonlinear Dynamics (NODY) journal. arXiv admin note: text overlap with arXiv:1009.1993 by other authors

References in corpus (6)

• Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
• A new dynamical model for the study of galactic structure
• Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits
• Using the S(c) spectrum to distinguish between order and chaos in a 3D galactic potential
• Periodic orbits in warped disk
• Chaotic orbits in a 3D galactic dynamical model with a double nucleus

Cited by in corpus (10)

• 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
• The Fast Norm Vector Indicator (FNVI) method: A new dynamical parameter for detecting order and chaos in Hamiltonian systems
• Determining the nature of orbits in disk galaxies with non spherical nuclei
• Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?
• Determining the type of orbits in the central regions of barred galaxies
• Exploring the origin, the nature and the dynamical behaviour of distant stars in galaxy models