In this work, we study a generic squared symmetric Hamiltonian of two degrees of freedom. Our aim is to show a global methodology to analyze the evolution of the families of periodic orbits and their bifurcations. To achieve it, we use several numerical techniques such as a systematic grid search algorithm in sequential and parallel, a fast chaos indicator and a tool for the continuation of periodic orbits. Using them, we are able to study the special and generic bifurcations of multiplicity one that allow us to understand the dynamics of the system and we show in detail the evolution of some symmetric breaking periodic orbits.

Abstract. Using detailed Monte Carlo radiative transfer simulations in realistic models for galactic nuclei, we critically investigate the influence of interstellar dust in ionised gas discs on the rotation curves and the resulting black hole mass measurements. We find that absorption and scattering by interstellar dust leaves the shape of the rotation curves basically unaltered, but slightly decreases the central slope of the rotation curves. As a result, the "observed" black hole masses are systematically underestimated by some 10 to 20% for realistic optical depths.