1. CMB Online first
2. CMB 2016 (vol 60 pp. 411)
 Stoyanov, Luchezar

On Gibbs Measures and Spectra of Ruelle Transfer Operators
We prove a comprehensive version of the RuellePerronFrobenius
Theorem
with explicit estimates of the spectral radius of the Ruelle
transfer operator and various other
quantities related to spectral properties of this operator. The
novelty here is that the HÃ¶lder
constant of the function generating the operator appears only
polynomially, not exponentially as
in previous known estimates.
Keywords:subshift of finite type, Ruelle transfer operator, Gibbs measure Categories:37A05, 37B10 

3. CMB 2015 (vol 59 pp. 95)
 Gonçalves, Daniel; Li, Hui; Royer, Danilo

Faithful Representations of Graph Algebras via Branching Systems
We continue to investigate branching systems of directed graphs
and their connections with graph algebras. We give a sufficient
condition under which the representation induced from a branching
system of a directed graph is faithful and construct a large
class of branching systems that satisfy this condition. We finish
the paper by providing a proof of the converse of the CuntzKrieger
uniqueness theorem for graph algebras by means of branching systems.
Keywords:C*algebra, graph algebra, Leavitt path algebra, branching system, representation Categories:46L05, 37A55 

4. CMB 2014 (vol 57 pp. 511)
 Gonçalves, Daniel

Simplicity of Partial Skew Group Rings of Abelian Groups
Let $A$ be a ring with local units, $E$ a set of local units for $A$,
$G$ an abelian group and $\alpha$ a partial action of $G$ by ideals of
$A$ that contain local units.
We show that $A\star_{\alpha} G$ is simple if and only if $A$ is
$G$simple and the center of the corner $e\delta_0 (A\star_{\alpha} G)
e \delta_0$ is a field for all $e\in E$. We apply the result to
characterize simplicity of partial skew group rings in two cases,
namely for partial skew group rings arising from partial actions by
clopen subsets of a compact set and partial actions on the set level.
Keywords:partial skew group rings, simple rings, partial actions, abelian groups Categories:16S35, 37B05 

5. CMB 2012 (vol 57 pp. 240)
 Bernardes, Nilson C.

Addendum to ``Limit Sets of Typical Homeomorphisms''
Given an integer $n \geq 3$,
a metrizable compact topological $n$manifold $X$ with boundary,
and a finite positive Borel measure $\mu$ on $X$,
we prove that for the typical homeomorphism $f : X \to X$,
it is true that for $\mu$almost every point $x$ in $X$ the restriction of
$f$ (respectively of $f^{1}$) to the omega limit set $\omega(f,x)$
(respectively to the alpha limit set $\alpha(f,x)$) is topologically
conjugate to the universal odometer.
Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets Categories:37B20, 54H20, 28C15, 54C35, 54E52 

6. CMB 2012 (vol 56 pp. 477)
 Ayadi, Adlene

Hypercyclic Abelian Groups of Affine Maps on $\mathbb{C}^{n}$
We give a characterization of hypercyclic abelian group
$\mathcal{G}$ of affine maps on $\mathbb{C}^{n}$. If $\mathcal{G}$
is finitely generated, this characterization is explicit. We prove
in particular
that no abelian group generated by $n$ affine maps on $\mathbb{C}^{n}$ has a dense orbit.
Keywords:affine, hypercyclic, dense, orbit, affine group, abelian Categories:37C85, 47A16 

7. CMB 2012 (vol 56 pp. 709)
 Bartošová, Dana

Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
It is a wellknown fact, that the greatest ambit for
a topological group $G$ is the Samuel compactification of $G$ with
respect to the right uniformity on $G.$ We apply the original
description by Samuel from 1948 to give a simple computation of the
universal minimal flow for groups of automorphisms of uncountable
structures using FraÃ¯ssÃ© theory and Ramsey theory. This work
generalizes some of the known results about countable structures.
Keywords:universal minimal flows, ultrafilter flows, Ramsey theory Categories:37B05, 03E02, 05D10, 22F50, 54H20 

8. CMB 2011 (vol 56 pp. 136)
 Munteanu, RaduBogdan

On Constructing Ergodic Hyperfinite Equivalence Relations of NonProduct Type
Product type equivalence relations are hyperfinite measured
equivalence relations, which, up to orbit equivalence, are generated
by product type odometer actions. We give a concrete example of a
hyperfinite equivalence relation of nonproduct type, which is the
tail equivalence on a Bratteli diagram.
In order to show that the equivalence relation constructed is not of
product type we will use a criterion called property A. This
property, introduced by Krieger for nonsingular transformations, is
defined directly for hyperfinite equivalence relations in this paper.
Keywords:property A, hyperfinite equivalence relation, nonproduct type Categories:37A20, 37A35, 46L10 

9. CMB 2011 (vol 55 pp. 858)
 von Renesse, MaxK.

An Optimal Transport View of SchrÃ¶dinger's Equation
We show that the SchrÃ¶dinger equation is a lift of Newton's third law
of motion $\nabla^\mathcal W_{\dot \mu} \dot \mu = \nabla^\mathcal W F(\mu)$ on
the space of probability measures, where derivatives are taken
with respect to the Wasserstein Riemannian metric. Here the potential
$\mu \to F(\mu)$ is the sum of the total classical potential energy $\langle V,\mu\rangle$
of the extended system
and its Fisher information
$ \frac {\hbar^2} 8 \int \nabla \ln \mu ^2
\,d\mu$. The precise relation is established via a wellknown
(Madelung) transform which is shown to be a symplectic submersion
of the standard symplectic
structure of complex valued functions into the
canonical symplectic space over the Wasserstein space.
All computations are conducted in the framework of Otto's formal
Riemannian calculus for optimal transportation of probability
measures.
Keywords:SchrÃ¶dinger equation, optimal transport, Newton's law, symplectic submersion Categories:81C25, 82C70, 37K05 

10. CMB 2011 (vol 55 pp. 708)
11. CMB 2011 (vol 55 pp. 297)
 Glasner, Eli

The Group $\operatorname{Aut}(\mu)$ is Roelcke Precompact
Following a similar result of Uspenskij on the unitary group of a
separable Hilbert space, we show that, with respect to the lower (or
Roelcke) uniform structure, the Polish group $G=
\operatorname{Aut}(\mu)$ of automorphisms of an atomless standard
Borel probability space $(X,\mu)$ is precompact. We identify the
corresponding compactification as the space of Markov operators on
$L_2(\mu)$ and deduce that the algebra of right and left uniformly
continuous functions, the algebra of weakly almost periodic functions,
and the algebra of Hilbert functions on $G$, i.e., functions on
$G$ arising from unitary representations, all coincide. Again
following Uspenskij, we also conclude that $G$ is totally minimal.
Keywords:Roelcke precompact, unitary group, measure preserving transformations, Markov operators, weakly almost periodic functions Categories:54H11, 22A05, 37B05, 54H20 

12. CMB 2011 (vol 55 pp. 225)
 Bernardes, Nilson C.

Limit Sets of Typical Homeomorphisms
Given an integer $n \geq 3$, a metrizable compact
topological $n$manifold $X$ with boundary, and a finite positive Borel
measure $\mu$ on $X$, we prove that for the typical homeomorphism
$f \colon X \to X$, it is true that for $\mu$almost every point $x$ in $X$
the limit set $\omega(f,x)$ is a Cantor set of Hausdorff dimension zero,
each point of $\omega(f,x)$ has a dense orbit in $\omega(f,x)$, $f$ is
nonsensitive at each point of $\omega(f,x)$, and the function
$a \to \omega(f,a)$ is continuous at $x$.
Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets Categories:37B20, 54H20, 28C15, 54C35, 54E52 

13. CMB 2011 (vol 54 pp. 676)
 Hammerlindl, Andy

Quasiisometry and Plaque Expansiveness
We show that a partially hyperbolic diffeomorphism is plaque
expansive (a form of structural stability for its center foliation) if the
strong stable and unstable foliations are quasiisometric in the universal
cover. In particular, all partially hyperbolic diffeomorphisms on the 3torus
are plaque expansive.
Category:37D30 

14. CMB 2011 (vol 54 pp. 311)
15. CMB 2009 (vol 53 pp. 295)
 Guo, Boling; Huo, Zhaohui

The Global Attractor of a Damped, Forced Hirota Equation in $H^1$
The existence of the global attractor of a damped
forced Hirota equation in the phase space $H^1(\mathbb R)$ is proved. The
main idea is to establish the socalled asymptotic compactness
property of the solution operator by energy equation approach.
Keywords:global attractor, Fourier restriction norm, damping system, asymptotic compactness Categories:35Q53, 35B40, 35B41, 37L30 

16. CMB 2008 (vol 51 pp. 545)
 Ionescu, Marius; Watatani, Yasuo

$C^{\ast}$Algebras Associated with MauldinWilliams Graphs
A MauldinWilliams graph $\mathcal{M}$ is a generalization of an
iterated function system by a directed graph. Its invariant set $K$
plays the role of the selfsimilar set. We associate a $C^{*}$algebra
$\mathcal{O}_{\mathcal{M}}(K)$ with a MauldinWilliams graph $\mathcal{M}$
and the invariant set $K$, laying emphasis on the singular points.
We assume that the underlying graph $G$ has no sinks and no sources.
If $\mathcal{M}$ satisfies the open set condition in $K$, and $G$
is irreducible and is not a cyclic permutation, then the associated
$C^{*}$algebra $\mathcal{O}_{\mathcal{M}}(K)$ is simple and purely
infinite. We calculate the $K$groups for some examples including the
inflation rule of the Penrose tilings.
Categories:46L35, 46L08, 46L80, 37B10 

17. CMB 2007 (vol 50 pp. 418)
18. CMB 2006 (vol 49 pp. 203)
 Çömez, Doğan

The Ergodic Hilbert Transform for Admissible Processes
It is shown that the ergodic Hilbert transform
exists for a class of bounded symmetric admissible processes
relative to invertible measure preserving transformations. This
generalizes the wellknown result on the existence of the ergodic
Hilbert transform.
Keywords:Hilbert transform, admissible processes Categories:28D05, 37A99 

19. CMB 2005 (vol 48 pp. 302)
20. CMB 2005 (vol 48 pp. 3)
 Burq, N.

Quantum Ergodicity of Boundary Values of Eigenfunctions: A Control Theory Approach
Consider $M$, a bounded domain in ${\mathbb R}^d$, which is a
Riemanian manifold with piecewise smooth boundary and suppose that the
billiard associated to the geodesic flow reflecting on the boundary
according to the laws of geometric optics is ergodic.
We prove that the boundary value of the eigenfunctions of the Laplace
operator with reasonable boundary conditions are asymptotically
equidistributed in the boundary, extending previous results by
G\'erard and Leichtnam as well as Hassell and Zelditch,
obtained under the additional assumption of the convexity of~$M$.
Categories:35Q55, 35BXX, 37K05, 37L50, 81Q20 

21. CMB 2004 (vol 47 pp. 553)
 Kerr, David

A Geometric Approach to VoiculescuBrown Entropy
A basic problem in dynamics is to identify systems
with positive entropy, i.e., systems which are ``chaotic.'' While
there is a vast collection of results addressing this issue in
topological dynamics, the phenomenon of positive entropy remains by and
large a mystery within the broader noncommutative domain of $C^*$algebraic
dynamics. To shed some light on the noncommutative situation we propose
a geometric perspective inspired by work of Glasner and Weiss on
topological entropy.
This is a written version of the author's talk
at the Winter 2002 Meeting of the Canadian Mathematical Society
in Ottawa, Ontario.
Categories:46L55, 37B40 

22. 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 

23. 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 

24. 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 

25. 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 
