Quantitative predictions with detuned normal forms

Details Quantitative predictions with detuned normal forms Quantitative predictions with detuned normal forms

2008-04-15

arxiv.org/abs/0804.2347v1

Celestial Mechanics & Dynamical Astronomy (2008), vol. 102, pp. 163--176

Nonlinear Sciences

Chaotic Dynamics

Accepted for publication on Celestial Mechanics and Dynamical Astronomy

Scientific paper

10.1007/s10569-008-9141-x

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.

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