- Nonlinear phenomena, like complex instability, inverse
bifurcations, and collisions of bifurcations, dominate the
dynamics of rotating triaxial potentials.
- For Sb and Sc galaxies the best self-consistent orbital stellar
model is a nonlinear one
ending at the 4:1 resonance. For Sa galaxies the stellar spiral arms
are weak and the best theoretical orbital model is a linear one ending at
- The above results hold for gaseous SPH models as well. In addition
the "4:1 resonance" models are also superior to models assuming the
end of the strong, symmetric spirals at the OLR.
- The use of color and rotation is an efficient method to visualize the
four-dimensional "space" of section in 3D Hamiltonian
systems. The neighborhood of stable, simple unstable, double
unstable and complex unstable periodic orbits has in each case
a characteristic fingerprint.
- Stable 3D periodic orbits with elliptical projections on the
equatorial plane can support a spiral pattern with variable
thickness. The edge-on shapes of orbits of these thick
spirals are determined by the vertical resonances existing in the potential.
- The addition of an m=1 component in a bisymmetric spiral
potential brings striking similarities between the morphology
of open grand design spiral galaxies and the corresponding
SPH, "4:1 resonance" models.
- The bar of NGC4314 is built by nonperiodic orbits trapped around
the stable periodic orbits of the x1 family. The boxy
structure at the end of the bar is due to chaotic orbits.
- The method of dynamical spectra is efficient in detecting tiny ordered domains
embedded in big chaotic seas.
- Many spiral galaxies show grand design spiral structure in K' although
several have a flocculent appearance on blue images suggesting that
stellar and gaseous disks are decoupled.
- Comparing the extent of the spiral pattern in K' in the galaxies
NGC3223, NGC5085, NGC5247, NGC5861, and NGC7083
with their angular velocity curves, the best agreement was obtained when
the symmetric, two-armed spiral starts just outside ILR and terminates
around the 4:1 resonance.
- In N-body simulations, non-linear spiral modes
last from four to seven pattern rotations and secure a grand-design
morphology to the models. Their dynamical behavior includes the
termination of the strong, symmetric, logarithmic stellar spirals inside
their 4:1 resonance radius, as foreseen from the orbital theory and from
SPH gasdynamical models.
- In SPH models of barred galaxies, the
longer lasting (for about 10 rotational periods of the bar) sharply
described shocks, occur if we assume a sound speed 20 km/s. The sound
speed influences the inflow rate of gas in barred
galaxies. Strong shocks occur close to the ends of the bar and
form "T-shaped" features.
- The amount of light coming from Brgamma and H2 emission represents only a few
percent of the observed K' light. A major contribution from young objects
in K' comes from continuum radiation which in the arm regions
can amount to 20%.
- In a 3D bar, the backbone of the
orbital structure is not just the x1 family, as in two-dimensional (2D)
models, but a tree of 2D and 3D families bifurcating from x1.
- The presence of a bar is not a sine qua non condition for the appearance of
boxy bulges, as often assumed. A `boxy' or a `peanut'
structure in the central parts of a model is due to the presence of
vertical resonances at which stable families of periodic orbits
bifurcate from the planar x1 family.
- A boxy/peanut feature can be built by 3D
families associated with 3D bifurcations of the x1 family. The `X'
feature observed inside the boxy bulges of several edge-on galaxies can
be attributed to the peaks of successive x1v1 orbits, provided their
stability allows it.
- 3D orbits that are introduced due to vertical instabilities play
a crucial role in the face-on profiles of bars and enhance their
- Inner rings in barred spiral galaxies are associated with
specific 2D and 3D families of periodic orbits located just beyond the
end of the bar. These are families located between the inner radial
ultraharmonic 4:1 resonance and corotation. The ring shapes that
are favoured are mainly ovals, as well as polygons
with `corners' on the minor axis, on the sides of the bar.
- Deep surface photometry in the K band obtained for 54 normal spiral
galaxies, shows that bulges are best represented by a Sersic law with
an index in the typical range of 1-2. Bars down to the detection
level at a relative amplitude of 3% were detected in 26 of 30
galaxies. The sample shows a lack of strong, tight spirals
which could indicate that such patterns are damped by
non-linear, dynamical effects due to their high radial force perturbations.
- Different bar morphologies may have as a backbone the same set
of x1 periodic orbits.
- In two-dimensional models with sufficiently large bar axial
ratios (a/c>6), stable orbits having propeller shapes play the
- Particle Swarm Optimization (PSO) is an efficient alternative method
for locating periodic orbits in a three-dimensional (3D) model of barred
- The subtraction from the images of boxy edge-on galaxies of a model
representing the axisymmetric component reveals the
contribution of the non-axisymmetric terms. There is a direct
correspondence between the orbital profiles of 3D bars in models and the
observed main morphological features of the residuals.
- The barred spiral galaxy NGC 3359 contains two pattern
speeds. The best match of models with observed data
indicates a pattern speed for the bar of 39.17 km/sec/kpc and
a value between 10 and 16 km/sec/kpc for the
- There are three types of orbits beyond corotation: Ordered
(periodic or quasi periodic), Chaotic, and Escaping. The
images of the x-axis on the (x, xdot) surface of section are along
certain ``rays'' and ``bell-type'' curves.
- The part of the spirals attached to the bar in many cases of
barred spiral galaxies, is due to
chaotic orbits. They are of the same type of
orbits that is responsible for the boxiness of the outer isophotes of the
bar in cases like NGC4314.