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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.
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 solution
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does not fully
For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how sm
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 latt
Let $X$ be a complex analytic manifold, $Dsubset X$ a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), $j: U=X-D to X$ the corresponding open inclusion, $E$ an integrable logarithmic connection with res