26. CMB 2004 (vol 47 pp. 332)
 Charette, Virginie; Goldman, William M.; Jones, Catherine A.

Recurrent Geodesics in Flat Lorentz $3$Manifolds
Let $M$ be a complete flat Lorentz $3$manifold $M$ with purely
hyperbolic holonomy $\Gamma$. Recurrent geodesic rays are completely
classified when $\Gamma$ is cyclic. This implies that for any pair of
periodic geodesics $\gamma_1$, $\gamma_2$, a unique geodesic forward
spirals towards $\gamma_1$ and backward spirals towards $\gamma_2$.
Keywords:geometric structures on lowdimensional manifolds, notions of recurrence Categories:57M50, 37B20 

27. CMB 2004 (vol 47 pp. 168)
 Baake, Michael; Sing, Bernd

Kolakoski$(3,1)$ Is a (Deformed) Model Set
Unlike the (classical) Kolakoski sequence on the alphabet $\{1,2\}$, its analogue
on $\{1,3\}$ can be related to a primitive substitution rule. Using this connection,
we prove that the corresponding biinfinite fixed point is a regular generic model set
and thus has a pure point diffraction spectrum. The Kolakoski$(3,1)$ sequence is
then obtained as a deformation, without losing the pure point diffraction property.
Categories:52C23, 37B10, 28A80, 43A25 

28. CMB 2003 (vol 46 pp. 277)
 Rochon, Frédéric

Rigidity of Hamiltonian Actions
This paper studies the following question: Given an
$\omega'$symplectic action of a Lie group on a manifold $M$ which
coincides, as a smooth action, with a Hamiltonian $\omega$action,
when is this action a Hamiltonian $\omega'$action? Using a result of
MorseBott theory presented in Section~2, we show in Section~3 of this
paper that such an action is in fact a Hamiltonian $\omega'$action,
provided that $M$ is compact and that the Lie group is compact and
connected. This result was first proved by LalondeMcDuffPolterovich
in 1999 as a consequence of a more general theory that made use of
hard geometric analysis. In this paper, we prove it using classical
methods only.
Categories:53D05, 37J25 

29. CMB 2002 (vol 45 pp. 697)
 Sirvent, V. F.; Solomyak, B.

Pure Discrete Spectrum for Onedimensional Substitution Systems of Pisot Type
We consider two dynamical systems associated with a substitution of
Pisot type: the usual $\mathbb{Z}$action on a sequence space, and
the $\mathbb{R}$action, which can be defined as a tiling dynamical
system or as a suspension flow. We describe procedures for checking
when these systems have pure discrete spectrum (the ``balanced
pairs algorithm'' and the ``overlap algorithm'') and study the
relation between them. In particular, we show that pure discrete
spectrum for the $\mathbb{R}$action implies pure discrete spectrum
for the $\mathbb{Z}$action, and obtain a partial result in the
other direction. As a corollary, we prove pure discrete spectrum
for every $\mathbb{R}$action associated with a twosymbol
substitution of Pisot type (this is conjectured for an arbitrary
number of symbols).
Categories:37A30, 52C23, 37B10 

30. CMB 2002 (vol 45 pp. 123)
 Moody, Robert V.

Uniform Distribution in Model Sets
We give a new measuretheoretical proof of the uniform distribution
property of points in model sets (cut and project sets). Each model
set comes as a member of a family of related model sets, obtained by
joint translation in its ambient (the `physical') space and its
internal space. We prove, assuming only that the window defining the
model set is measurable with compact closure, that almost surely the
distribution of points in any model set from such a family is uniform
in the sense of Weyl, and almost surely the model set is pure point
diffractive.
Categories:52C23, 11K70, 28D05, 37A30 

31. CMB 2001 (vol 44 pp. 292)
 McKay, Angela

An Analogue of Napoleon's Theorem in the Hyperbolic Plane
There is a theorem, usually attributed to Napoleon, which states that
if one takes any triangle in the Euclidean Plane, constructs
equilateral triangles on each of its sides, and connects the midpoints
of the three equilateral triangles, one will obtain an equilateral
triangle. We consider an analogue of this problem in the hyperbolic
plane.
Category:37D40 
