97 research outputs found
Packing dimensions of the divergence points of self-similar measures with the open set condition
Let be the self-similar measure supported on the self-similar set
with open set condition. In this article, we discuss the packing dimension of
the set for
, where denotes the
set of accumulation points of \frac{\log\mu(B(x,r))}{\log r}r\searrow0$.
Our main result solves the conjecture about packing dimension posed by Olsen
and Winter \cite{OlsWin} and generalizes the result in \cite{BaeOlsSni}.Comment: 13 page
Multifractal Analysis of Ergodic Averages in Some Nonuniformly Hyperbolic Systems
This article is devoted to the study of the multifractal analysis of ergodic
averages in some nonuniformly hyperbolic systems. In particular, our results
hold for the robust classes of multidimensional nonuniformly expanding local
diffeomorphisms and Viana maps.Comment: 15 page
Multifractal analysis for historic set in topological dynamical systems
In this article, the historic set is divided into different level sets and we
use topological pressure to describe the size of these level sets. We give an
application of these results to dimension theory. Especially, we use
topological pressure to describe the relative multifractal spectrum of ergodic
averages and give a positive answer to the conjecture posed by L. Olsen (J.
Math. Pures Appl. {\bf 82} (2003)).Comment: 30 page
The variational principle of local pressure for actions of sofic group
This study establishes the variational principle for local pressure in the
sofic context.Comment: 13 page
The Bowen's topological entropy of the Cartesian product sets
This article is devoted to showing the product theorem for Bowen's
topological entropy.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1012.1103 by
other author
Commutators of multilinear singular integral operators on non-homogeneous metric measure spaces
Let be a metric measure space satisfying both the geometrically
doubling and the upper doubling measure conditions, which is called
non-homogeneous metric measure space. In this paper, via a sharp maximal
operator, the boundedness of commutators generated by multilinear singular
integral with function on non-homogeneous metric measure spaces in
-multiple Lebesgue spaces is obtained.Comment: 17 page
The Historic Set of Ergodic Averages in Some Nonuniformly Hyperbolic Systems
This article is devoted to the study of the historic set of ergodic averages
in some nonuniformly hyperbolic systems. In particular, our results hold for
the robust classes of multidimensional nonuniformly expanding local
diffeomorphisms and Viana maps.Comment: 18 pages. Comments are welcome. arXiv admin note: text overlap with
arXiv:1310.234
Topological pressure dimension for almost additive potentials
This paper is devoted to the study of the topological pressure dimension for
almost additive sequences, which is an extension of topological entropy
dimension. We investigate fundamental properties of the topological pressure
dimension for almost additive sequences. In particular, we study the
relationships among different types of topological pressure dimension and
identifies an inequality relating them. Also, we show that the topological
pressure dimension is always equal to or greater than 1 for certain special
almost additive sequence.Comment: 23 pages. arXiv admin note: text overlap with arXiv:1104.2195 by
other author
Positive topological entropy and -weakly mixing sets
The notion of -weakly mixing set is introduced, which shares similar
properties of weakly mixing sets. It is shown that if a dynamical system has
positive topological entropy, then the collection of -weakly mixing
sets is residual in the closure of the collection of entropy sets in the
hyperspace. The existence of -weakly mixing sets in a topological
dynamical system admitting an ergodic invariant measure which is not measurable
distal is obtained. Moreover, Our results generalize several well known results
and also answer several open questions.Comment: 26 page
Topological pressure, mistake functions and average metric
In this paper, we showed that the Pesin pressure of any subset under a
mistake function is equal to the classical Pesin pressure of the subset in
dynamical systems. Our result extended the result of [1] in additive case,
which proved the topological pressure of the whole system is self adaptable
under a mistake function. As an application, we showed that the Pesin pressure
defined by average metric is equal to the classical Pesin pressure.Comment: 7 page
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