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We investigate the dynamics in the logarithmic galactic potential with ananalytical approach. The phase-space structure of the real system isapproximated with resonant detuned normal forms constructed with the methodbased on the Lie transform. Attention is focused on the properties of the axialperiodic orbits and of low order `boxlets' that play an important role ingalactic models. Using energy and ellipticity as parameters, we find analyticalexpressions of several useful indicators, such as stability-instabilitythresholds, bifurcations and phase-space fractions of some orbit families andcompare them with numerical results available in the literature.

On the Orbit Structure of the Logarithmic Potential