Pitch Angle Restrictions in Late Type Spiral Galaxies Based on Chaotic
  and Ordered Orbital Behavior
  We built models for low bulge mass spiral galaxies (late type as defined by
the Hubble classification) using a 3-D self-gravitating model for spiral arms,
and analyzed the orbital dynamics as a function of pitch angle, going from
10$\deg$ to 60$\deg$. Testing undirectly orbital self-consistency, we search
for the main periodic orbits and studied the density response. For pitch angles
up to approximately $\sim 20\deg$, the response supports closely the potential
permitting readily the presence of long lasting spiral structures. The density
response tends to "avoid" larger pitch angles in the potential, by keeping
smaller pitch angles in the corresponding response. Spiral arms with pitch
angles larger than $\sim 20\deg$, would not be long-lasting structures but
rather transient. On the other hand, from an extensive orbital study in phase
space, we also find that for late type galaxies with pitch angles larger than
$\sim 50\deg$, chaos becomes pervasive destroying the ordered phase space
surrounding the main stable periodic and quasi-periodic orbits and even
destroying them. This result is in good agreement with observations of late
type galaxies, where the maximum observed pitch angle is $\sim 50\deg$.
