60,018 research outputs found
Definable Topological Dynamics in Metastable Theories
We initiate a study of the definable topological dynamics of groups definable in metastable theories. In stable theories, it is known that the quotient of a group G by its type-definable connected component G00 is isomorphic to the Ellis Group of the flow (G(M),SG(M)); we consider whether these results could be extended to the broader metastable setting. Further, the definable topological dynamics of compactly dominated groups in the o-minimal setting is well understood. We investigate to what extent stable domination is a suitable analogue of compact domination in regards to describing the Ellis Group of metastable definable group
Consensus formation on coevolving networks: groups' formation and structure
We study the effect of adaptivity on a social model of opinion dynamics and
consensus formation. We analyze how the adaptivity of the network of contacts
between agents to the underlying social dynamics affects the size and
topological properties of groups and the convergence time to the stable final
state. We find that, while on static networks these properties are determined
by percolation phenomena, on adaptive networks the rewiring process leads to
different behaviors: Adaptive rewiring fosters group formation by enhancing
communication between agents of similar opinion, though it also makes possible
the division of clusters. We show how the convergence time is determined by the
characteristic time of link rearrangement. We finally investigate how the
adaptivity yields nontrivial correlations between the internal topology and the
size of the groups of agreeing agents.Comment: 10 pages, 3 figures,to appear in a special proceedings issue of J.
Phys. A covering the "Complex Networks: from Biology to Information
Technology" conference (Pula, Italy, 2007
The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group
To any automorphism, , of a totally disconnected, locally compact
group, , there is associated a compact, -stable subgroup of ,
here called the \emph{nub} of , on which the action of is
topologically transitive. Topologically transitive actions of automorphisms of
compact groups have been studied extensively in topological dynamics and
results obtained transfer, via the nub, to the study of automorphisms of
general locally compact groups.
A new proof that the contraction group of is dense in the nub is
given, but it is seen that the two-sided contraction group need not be dense.
It is also shown that each pair , with compact and
topologically transitive, is an inverse limit of pairs that have `finite depth'
and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold
for pairs with finite depth
Shape of matchbox manifolds
In this work, we develop shape expansions of minimal matchbox manifolds
without holonomy, in terms of branched manifolds formed from their leaves. Our
approach is based on the method of coding the holonomy groups for the foliated
spaces, to define leafwise regions which are transversely stable and are
adapted to the foliation dynamics. Approximations are obtained by collapsing
appropriately chosen neighborhoods onto these regions along a "transverse
Cantor foliation". The existence of the "transverse Cantor foliation" allows us
to generalize standard techniques known for Euclidean and fibered cases to
arbitrary matchbox manifolds with Riemannian leaf geometry and without
holonomy. The transverse Cantor foliations used here are constructed by purely
intrinsic and topological means, as we do not assume that our matchbox
manifolds are embedded into a smooth foliated manifold, or a smooth manifold.Comment: 36 pages. Revision of the earlier version: introduction is rewritten.
Accepted to a special issue of Indagationes Mathematica
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