224 research outputs found
Relationship between Li-Yorke chaos and positive topological sequence entropy in nonautonomous dynamical systems
We study chaotic properties of uniformly convergent nonautonomous dynamical
systems. We show that, contrary to the autonomous systems on the compact
interval, positivity of topological sequence entropy and occurrence of Li-Yorke
chaos are not equivalent, more precisely, neither of the two possible
implications is true.Comment: 10 pages, 4 figure
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
Metric Entropy of Nonautonomous Dynamical Systems
We introduce the notion of metric entropy for a nonautonomous dynamical
system given by a sequence of probability spaces and a sequence of
measure-preserving maps between these spaces. This notion generalizes the
classical concept of metric entropy established by Kolmogorov and Sinai, and is
related via a variational inequality to the topological entropy of
nonautonomous systems as defined by Kolyada, Misiurewicz and Snoha. Moreover,
it shares several properties with the classical notion of metric entropy. In
particular, invariance with respect to appropriately defined isomorphisms, a
power rule, and a Rokhlin-type inequality are proved
Entropy of homeomorphisms on unimodal inverse limit spaces
We prove that every self-homeomorphism on the inverse limit
space of the tent map with slope has
topological entropy \htop(h) = |R| \log s, where is such that
and are isotopic. Conclusions on the possible values of the entropy
of homeomorphisms of the inverse limit space of a (renormalizable) quadratic
map are drawn as well
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