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Register a new userPeriodic orbits in the logarithmic potential
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Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms. The solutions of the equations of motion corresponding to periodic orbits are obtained as series expansions computed by inverting the normalizing canonical transformation. To improve the convergence of the series a resummation based on a continued fraction may be performed. This method is analogous to that looking for approximate rational solutions (Prendergast method). It is shown that with a normal form truncated at the lowest order incorporating the relevant resonance it is possible to construct quite accurate solutions both for normal modes and periodic orbits in general position.
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We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie transform. Attention is focused on the properties of the axial periodic orbits and of low order `boxlets that play an important role in galactic models. Using energy and ellipticity as parameters, we find analytical expressions of several useful indicators, such as stability-instability thresholds, bifurcations and phase-space fractions of some orbit families and compare them with numerical results available in the literature.
We establish a formula relating global diffusion in a space periodic dynamical system to cycles in the elementary cell which tiles the space under translations.
Gutzwillers trace formula and Bogomolnys formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.
We study the orbits in a Manko-Novikov type metric (MN) which is a perturbed Kerr metric. There are periodic, quasi-periodic, and chaotic orbits, which are found in configuration space and on a surface of section for various values of the energy E and the z-component of the angular momentum Lz. For relatively large Lz there are two permissible regions of non-plunging motion bounded by two closed curves of zero velocity (CZV), while in the Kerr metric there is only one closed CZV of non-plunging motion. The inner permissible region of the MN metric contains mainly chaotic orbits, but it contains also a large island of stability. We find the positions of the main periodic orbits as functions of Lz and E, and their bifurcations. Around the main periodic orbit of the outer region there are islands of stability that do not appear in the Kerr metric. In a realistic binary system, because of the gravitational radiation, the energy E and the angular momentum Lz of an inspiraling compact object decrease and therefore the orbit of the object is non-geodesic. In fact in an EMRI system the energy E and the angular momentum Lz decrease adiabatically and therefore the motion of the inspiraling object is characterized by the fundamental frequencies which are drifting slowly in time. In the Kerr metric the ratio of the fundamental frequencies changes strictly monotonically in time. However, in the MN metric when an orbit is trapped inside an island the ratio of the fundamental frequencies remains constant for some time. Hence, if such a phenomenon is observed this will indicate that the system is non integrable and therefore the central object is not a Kerr black hole.
A coherently oscillating real scalar field with potential shallower than quadratic one fragments into spherical objects called I-balls. We study the I-ball formation for logarithmic potential which appears in many cosmological models. We perform lattice simulations and find that the I-balls are formed when the potential becomes dominated by the quadratic term. Furthermore, we estimate the I-ball profile assuming that the adiabatic invariant is conserved during formation and obtain the result that agrees to the numerical simulations.
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