Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits

We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in the 3D potential. Both 2D and 3D potentials display exact periodic orbits together with extended chaotic regions. Numerical experiments suggest, that the degree of chaos increases rapidly, as the energy of the test particle increases. About 97% of the phase plane of the 2D system is covered by chaotic orbits for large energies. The regular or chaotic character of the 2D orbits is checked using the S(c) dynamical spectrum, while for the 3D potential we use the S(c) spectrum, along with the P(f) spectral method. Comparison with other dynamical indicators shows that the S(c) spectrum gives fast and reliable information about the character of motion.Comment: Published in Nonlinear Dynamics (NODY) journa

Application of new dynamical spectra of orbits in Hamiltonian systems

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.Comment: Published in Nonlinear Dynamics (NODY) journal. arXiv admin note: text overlap with arXiv:1009.1993 by other author

Chaotic orbits in a galaxy model with a massive nucleus

The transition from regular to chaotic motion is studied in an axially symmetric galaxy model with a disk-halo and a spherical nucleus. This model has the characteristic that the mass of the nucleus increases exponentially, because mass is transported from the disk to the nucleus while the total mass of the galaxy remains constant. Stars with values of angular momentum Lz less or equal to a critical value $L_{z{\rm c}}$, moving near the galactic plane, are scattered to the halo when approaching the nucleus. The corresponding orbits are chaotic. A linear relationship is found to exist between the critical angular momentum and the final mass of the nucleus Mnf. Our results suggest that the stars in the central regions of disk galaxies with massive nuclei must be in chaotic orbits. Comparison with previous work is also made