Continuation and stability deduction of resonant periodic orbits in three dimensional systems

In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the classical three body problem in three dimensions and use its dynamics to assess the long-term evolution of extrasolar systems. We compute periodic orbits, which correspond to exact resonant motion, and determine their linear stability. By computing maps of dynamical stability we show that stable periodic orbits are surrounded in phase space with regular motion even in systems with more than two degrees of freedom, while chaos is apparent close to unstable ones. Therefore, families of stable periodic orbits, indeed, consist backbones of the stability domains in phase space.Comment: Proceedings of the 6th International Conference on Numerical Analysis (NumAn 2014). Published by the Applied Mathematics and Computers Lab, Technical University of Crete (AMCL/TUC), Greec

Higher-dimensional models in gravitational theories of quarticLagrangians

Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The spacetime consists of one timelike dimension and two maximally symmetric subspaces, filled with matter in the form of an anisotropic fluid. Numerical integration of the cosmological field equations indicates that exponential, as well as power law, solutions are possible. We carry out a dynamical study of the results in the H_{ext} - H_{int} plane and confirm the existence of "attractors" in the evolution of the Universe. Those attracting points correspond to "extended De Sitter" spacetimes, in which the external space exhibits inflationary expansion, while the internal one contracts.Comment: LaTeXfile, 22 page

Multi-Planet Destabilisation and Escape in Post-Main Sequence Systems

Discoveries of exoplanets orbiting evolved stars motivate critical examinations of the dynamics of $N$-body systems with mass loss. Multi-planet evolved systems are particularly complex because of the mutual interactions between the planets. Here, we study the underlying dynamical mechanisms which can incite planetary escape in two-planet post-main sequence systems. Stellar mass loss alone is unlikely to be rapid and high enough to eject planets at typically-observed separations. However, the combination of mass loss and planet-planet interactions can prompt a shift from stable to chaotic regions of phase space. Consequently, when mass loss ceases, the unstable configuration may cause escape. By assuming a constant stellar mass loss rate, we utilize maps of dynamical stability to illustrate the distribution of regular and chaotic trajectories in phase space. We show that chaos can drive the planets to undergo close encounters, leading to the ejection of one planet. Stellar mass loss can trigger the transition of a planetary system from a stable to chaotic configuration, subsequently causing escape. We find that mass loss non-adiabatically affects planet-planet interaction for the most massive progenitor stars which avoid the supernova stage. For these cases, we present specific examples of planetary escape.Comment: Accepted for publication in MNRAS (2013

Chaotic motion in multi-black hole spacetimes and holographic screens

We investigate the geodesic motion in $D-$dimensional Majumdar-Papapetrou multi-black hole spacetimes and find that the qualitative features of the D=4 case are shared by the higher dimensional configurations. The motion of timelike and null particles is chaotic, the phase space being divided into basins of attraction which are separated by a fractal boundary, with a fractal dimension $d_B$. The mapping of the geodesic trajectories on a screen placed in the asymptotic region is also investigated. We find that the fractal properties of the phase space induces a fractal structure on the holographic screen, with a fractal dimension $d_B-1$.Comment: 8 pages, 5 figure

Kinetic description of particle interaction with a gravitational wave

The interaction of charged particles, moving in a uniform magnetic field, with a plane-polarized gravitational wave is considered using the Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact locations in phase space, where resonance overlapping occurs. We investigate the diffusion of orbits around each primary resonance of order (m) by deriving general analytical expressions for an effective diffusion coeficient. A solution to the corresponding diffusion equation (Fokker-Planck equation) for the static case is found. Numerical integration of the full equations of motion and subsequent calculation of the diffusion coefficient verifies the analytical results.Comment: LaTeX file, 15 page