Quantitative predictions with detuned normal forms

Abstract

The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attention is focused on the quantitative predictive ability of the normal form. We find analytical expressions for bifurcations of periodic orbits and compare them with other analytical approaches and with numerical results. The predictions are quite reliable even outside the convergence radius of the perturbation and we analyze this result using resummation techniques of asymptotic series.

Accepted for publication on Celestial Mechanics and Dynamical Astronomy

References in corpus (2)

• On the Orbit Structure of the Logarithmic Potential
• Stability of axial orbits in galactic potentials

Cited by in corpus (13)

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• Resonances and bifurcations in systems with elliptical equipotentials
• Periodic orbits for a class of galactic potentials
• Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance
• Resonances and bifurcations in axisymmetric scale-free potentials
• Poincaré-like approach to Landau Theory. I. General theory
• Normal forms for the Laplace resonance
• The symmetric 1:2 resonance
• Periodic orbits of mechanical systems with homogeneous polynomial terms of degree five
• Resonant normal form and asymptotic normal form behavior in magnetic bottle Hamiltonians