741 research outputs found
Lowering topological entropy over subsets revisited
Let be a topological dynamical system. Denote by and the covering entropy and dimensional entropy of ,
respectively. is called D-{\it lowerable} (resp. {\it lowerable}) if
for each there is a subset (resp. closed subset)
with (resp. ); is called D-{\it hereditarily
lowerable} (resp. {\it hereditarily lowerable}) if each Souslin subset (resp.
closed subset) is D-lowerable (resp. lowerable).
In this paper it is proved that each topological dynamical system is not only
lowerable but also D-lowerable, and each asymptotically -expansive system is
D-hereditarily lowerable. A minimal system which is lowerable and not
hereditarily lowerable is demonstrated.Comment: All comments are welcome. Transactions of the American Mathematical
Society, to appea
Local entropy theory for a countable discrete amenable group action
In the paper we throw the first light on studying systematically the local
entropy theory for a countable discrete amenable group action. For such an
action, we introduce entropy tuples in both topological and measure-theoretic
settings and build the variational relation between these two kinds of entropy
tuples by establishing a local variational principle for a given finite open
cover. Moreover, based the idea of topological entropy pairs, we introduce and
study two special classes of such an action: uniformly positive entropy and
completely positive entropy. Note that in the building of the local variational
principle, following Romagnoli's ideas two kinds of measure-theoretic entropy
are introduced for finite Borel covers. These two kinds of entropy turn out to
be the same, where Danilenko's orbital approach becomes an inevitable tool
Dynamical compactness and sensitivity
To link the Auslander point dynamics property with topological transitivity,
in this paper we introduce dynamically compact systems as a new concept of a
chaotic dynamical system given by a compact metric space and a
continuous surjective self-map . Observe that each weakly mixing
system is transitive compact, and we show that any transitive compact M-system
is weakly mixing. Then we discuss the relationships among it and other several
stronger forms of sensitivity. We prove that any transitive compact system is
Li-Yorke sensitive and furthermore multi-sensitive if it is not proximal, and
that any multi-sensitive system has positive topological sequence entropy.
Moreover, we show that multi-sensitivity is equivalent to both thick
sensitivity and thickly syndetic sensitivity for M-systems. We also give a
quantitative analysis for multi-sensitivity of a dynamical system.Comment: This version is accepted by Journal of Differential Equations. arXiv
admin note: text overlap with arXiv:1504.0058
An experimental study of clogging fault diagnosis in heat exchangers based on vibration signals
The water-circulating heat exchangers employed in petrochemical industrials have attracted great attentions in condition monitoring and fault diagnosis. In this paper, an approach based on vibration signals is proposed. By the proposed method, vibration signals are collected for different conditions through various high-precision wireless sensors mounted on the surface of the heat exchanger. Furthermore, by analyzing the characteristics of the vibration signals, a database of fault patterns is established, which therefore provides a scheme for conditional monitoring of the heat exchanger. An experimental platform is set up to evaluate the feasibility and effectiveness of the proposed approach, and support vector machine based on dimensionless parameters is developed for fault classification. The results have shown that the proposed method is efficient and has achieved a high accuracy for benchmarking vibration signals under both normal and faulty conditions
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