30,174 research outputs found
Generic Points for Dynamical Systems with Average Shadowing
It is proved that to every invariant measure of a compact dynamical system
one can associate a certain asymptotic pseudo orbit such that any point
asymptotically tracing in average that pseudo orbit is generic for the measure.
It follows that the asymptotic average shadowing property implies that every
invariant measure has a generic point. The proof is based on the properties of
the Besicovitch pseudometric DB which are of independent interest. It is proved
among the other things that the set of generic points of ergodic measures is a
closed set with respect to DB. It is also showed that the weak specification
property implies the average asymptotic shadowing property thus the theory
presented generalizes most known results on the existence of generic points for
arbitrary invariant measures
On almost specification and average shadowing properties
In this paper we study relations between almost specification property,
asymptotic average shadowing property and average shadowing property for
dynamical systems on compact metric spaces. We show implications between these
properties and relate them to other important notions such as shadowing,
transitivity, invariant measures, etc. We provide examples that compactness is
a necessary condition for these implications to hold. As a consequence of our
methodology we also obtain a proof that limit shadowing in chain transitive
systems implies shadowing.Comment: 2 figure
Two results on entropy, chaos, and independence in symbolic dynamics
We survey the connections between entropy, chaos, and independence in
topological dynamics. We present extensions of two classical results placing
the following notions in the context of symbolic dynamics:
1. Equivalence of positive entropy and the existence of a large (in terms of
asymptotic and Shnirelman densities) set of combinatorial independence for
shift spaces.
2. Existence of a mixing shift space with a dense set of periodic points with
topological entropy zero and without ergodic measure with full support, nor any
distributionally chaotic pair.
Our proofs are new and yield conclusions stronger than what was known before.Comment: Comments are welcome! This preprint contains results from
arXiv:1401.5969v
The Ellis semigroup of a nonautonomous discrete dynamical system
We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical
system when is a metric compact space. The underlying
set of this semigroup is the pointwise closure of \{f\sp{n}_1 \, |\, n\in
\mathbb{N}\} in the space X\sp{X}.
By using the convergence of a sequence of points with respect to an
ultrafilter it is possible to give a precise description of the semigroup and
its operation. This notion extends the classical Ellis semigroup of a discrete
dynamical system. We show several properties that connect this semigroup and
the topological properties of the nonautonomous discrete dynamical system
Self-dual Maxwell field in 3D gravity with torsion
We study the system of self-dual Maxwell field coupled to 3D gravity with
torsion, with Maxwell field modified by a topological mass term. General
structure of the field equations reveals a new, dynamical role of the classical
central charges, and gives a simple correspondence between self-dual solutions
with torsion and their Riemannian counterparts. We construct two exact
self-dual solutions, corresponding to the sectors with massless and massive
Maxwell field, and calculate their conserved charges.Comment: LATEX, 15 pages, v2: minor correction
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