The stellar dynamics at the transitions between a strongly barred and
rotating potential and a spherical and dense central mass concentratio
n is investigated in a model potential. Three different degrees of con
centration of the central mass are studied. The main families of three
-dimensonal periodic orbit are found by numerical means. The structure
of phase space is presented by bifurcation diagrams and surfaces of s
ection. A large region of instability develops near the inner Lindblad
resonance (ILR) due to the strong bar potential. In such a mass confi
guration the radial ILR is typically near the corresponding vertical I
LR, consequently the instability of orbits is radial as well as vertic
al, helping the heating of disk stars into a bulge. These secular evol
ution processes from barred to unbarred and in the direction of increa
sing the bulge-to-disk ratio should affect the evolution of galaxies o
ver a Hubble time.