On the Orbit Structure of the Logarithmic Potential

Abstract

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.

To appear on the Astrophysical Journal

References in corpus (6)

• Triaxial Galaxies with Cusps
• Elliptical Galaxy Dynamics
• Cusps without chaos
• Periodic Orbits in Triaxial Galaxies with Weak Cusps
• Can galactic nuclei be non-axisymmetric? --- The parameter space of power-law discs
• Stability of axial orbits in galactic potentials

Cited by in corpus (11)

• Quantitative predictions with detuned normal forms
• Equivariant singularity analysis of the 2:2 resonance
• The role of the unstable equilibrium points in the transfer of matter in galactic potentials
• A Study of the Orbits of the Logarithmic Potential for Galaxies
• Natural orbit approximations in single power-law potentials
• Periodic orbits in the logarithmic potential
• Resonances and bifurcations in systems with elliptical equipotentials
• Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance
• Resonances and bifurcations in axisymmetric scale-free potentials
• The symmetric 1:2 resonance
• On the detuned 2:4 resonance