1. CMB 2006 (vol 49 pp. 337)
 Berlanga, R.

Homotopy Equivalence and Groups of MeasurePreserving Homeomorphisms
It is shown that the group of compactly
supported, measurepreserving homeomorphisms of a
connected, second countable manifold is locally contractible in the direct limit topology.
Furthermore, this group is weakly homotopically equivalent to the more general group of
compactly supported homeomorphisms.
Categories:57S05, 58F11 

2. CMB 2004 (vol 47 pp. 607)
 Plamenevskaya, Olga

A Residue Formula for $\SU(2)$Valued Moment Maps
Jeffrey and Kirwan gave expressions
for intersection pairings on the reduced space
$M_0=\mu^{1}(0)/G$ of a Hamiltonian $G$space $M$
in terms of multiple residues.
In this paper we prove a residue formula for
symplectic volumes of reduced spaces of a quasiHamiltonian
$\SU(2)$space. The definition of quasiHamiltonian
$G$spaces was recently introduced in .
Category:58F05 

3. CMB 2002 (vol 45 pp. 97)
 Haas, Andrew

Invariant Measures and Natural Extensions
We study ergodic properties of a family of interval maps that are
given as the fractional parts of certain real M\"obius
transformations. Included are the maps that are exactly
$n$to$1$, the classical Gauss map and the Renyi or backward
continued fraction map. A new approach is presented for deriving
explicit realizations of natural automorphic extensions and their
invariant measures.
Keywords:Continued fractions, interval maps, invariant measures Categories:11J70, 58F11, 58F03 

4. CMB 2001 (vol 44 pp. 323)
 Schuman, Bertrand

Une classe d'hamiltoniens polynomiaux isochrones
Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan
$\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones
qui sont des perturbations polynomiales de $H_0$. On obtient alors
une condition n\'ecessaire d'isochronisme, et un crit\`ere de choix
pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant
une g\'en\'eralisation du caract\`ere isochrone des perturbations
hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S].
Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the
plane $\Rset^2$. We obtain a necessary condition for a system to be
isochronous. We can think of this result as a generalization of the
isochronous behaviour of the homogeneous polynomial perturbation of
the Hamiltonian $H_0$ considered in [L], [P], [S].
Keywords:Hamiltonian system, normal forms, resonance, linearization Categories:34C20, 58F05, 58F22, 58F30 

5. CMB 2001 (vol 44 pp. 140)
 Gotay, Mark J.; Grabowski, Janusz

On Quantizing Nilpotent and Solvable Basic Algebras
We prove an algebraic ``nogo theorem'' to the effect that a
nontrivial \pa\ cannot be realized as an associative algebra with the
commu\ta\tor bracket. Using it, we show that there is an
obstruction to quantizing the \pa\ of polynomials generated by a
nilpotent \ba\ on a \sm. This result generalizes \gr 's famous
theorem on the impossibility of quantizing the Poisson algebra of
polynomials on $\r^{2n}$. Finally, we explicitly construct a
polynomial quantization of a \sm\ with a solvable \ba, thereby showing
that the obstruction in the nilpotent case does not extend to the
solvable case.
Categories:81S99, 58F06 

6. CMB 2001 (vol 44 pp. 129)
 CurrásBosch, Carlos

LinÃ©arisation symplectique en dimension 2
In this paper the germ of neighborhood of a compact leaf in a
Lagrangian foliation is symplectically classified when the compact
leaf is $\bT^2$, the affine structure induced by the Lagrangian
foliation on the leaf is complete, and the holonomy of $\bT^2$ in
the foliation linearizes. The germ of neighborhood is classified by a
function, depending on one transverse coordinate, this function is
related to the affine structure of the nearly compact leaves.
Keywords:symplectic manifold, Lagrangian foliation, affine connection Categories:53C12, 58F05 

7. CMB 2000 (vol 43 pp. 427)
 Ivey, Thomas A.

Helices, Hasimoto Surfaces and BÃ¤cklund Transformations
Travelling wave solutions to the vortex filament flow generated by
elastica produce surfaces in $\R^3$ that carry mutually orthogonal
foliations by geodesics and by helices. These surfaces are classified
in the special cases where the helices are all congruent or are all
generated by a single screw motion. The first case yields a new
characterization for the B\"acklund transformation for constant
torsion curves in $\R^3$, previously derived from the wellknown
transformation for pseudospherical surfaces. A similar investigation
for surfaces in $H^3$ or $S^3$ leads to a new transformation for
constant torsion curves in those spaces that is also derived from
pseudospherical surfaces.
Keywords:surfaces, filament flow, BÃ¤cklund transformations Categories:53A05, 58F37, 52C42, 58A15 

8. CMB 1997 (vol 40 pp. 271)