64 research outputs found
Topological entropy of sets of generic points for actions of amenable groups
Let be a countable discrete amenable group which acts continuously on a
compact metric space and let be an ergodic invariant Borel
probability measure on . For a fixed tempered F{\o}lner sequence
in with , we
prove the following variational principle:
where is the set of generic
points for with respect to and is the
Bowen topological entropy (along ) on . This generalizes the
classical result of Bowen in 1973.Comment: Science China Mathematics, 201
On the topological pressure of the saturated set with non-uniform structure
We derive a conditional variational principle of the saturated set for
systems with the non-uniform structure. Our result applies to a broad class of
systems including beta-shifts, S-gap shifts and their factors.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1605.07283; text
overlap with arXiv:1304.5497 by other author
Conditional Variational Principle for Historic Set in Some Nonuniformly Hyperbolic Systems
This article is devoted to the study of the historic set, which was
introduced by Ruelle, of Birkhoff averges in some nonuniformly hyperbolic
systems via Pesin theory. Particularly, we give a conditional variational
principle for historic sets. Our results can be applied (i) to the
diffeomorphisms on surfaces, (ii) to the nonuniformly hyperbolic
diffeomorphisms described by Katok and several other classes of diffeomorphisms
derived from Anosov systems.Comment: 22pages. arXiv admin note: substantial text overlap with
arXiv:1502.02459, arXiv:1412.076
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
Projection Pressure and Bowen's Equation for a Class of Self-similar Fractals with Overlap Structure
Let be an iterated function system(IFS) on
with attractor K. Let be the canonical projection. In this paper we
define a new concept called "projection pressure" for under certain affine IFS, and show the variational principle
about the projection pressure. Furthermore we check that the unique zero root
of "projection pressure" still satisfies Bowen's equation when each is
the similar map with the same compression ratio. Using the root of Bowen's
equation, we can get the Hausdorff dimension of the attractor
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
Relative tail entropy for random bundle transformations
We introduce the relative tail entropy to establish a variational principle
for continuous bundle random dynamical systems. We also show that the relative
tail entropy is conserved by the principal extension
Induced topological pressure for topological dynamical(to appear in JPM)
In this paper, inspired by the article [5], we introduce the induced
topological pressure for a topological dynamical system. In particular, we
prove a variational principle for the induced topological pressure
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
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
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