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Ercai Chen

Publications and source records attributed to Ercai Chen.

63 records · Page 4Linked to original sources
arXiv2012

Packing dimensions of the divergence points of self-similar measures with the open set condition

Let $μ$ be the self-similar measure supported on the self-similar set $K$ with open set condition. In this article, we discuss the packing dimension of the set $\{x\in K: A(\frac{\logμ(B(x,r))}{\log r})=I\}$ for $I\subseteq\mathbb{R}$, where $A(\frac{\logμ(B(x,r))}{\log r})$ denotes the set of accumulation points of \frac{\logμ(B(x,r))}{\log r}$ as $r\searrow0$. Our main result solves the conjecture about packing dimension posed by Olsen and Winter \cite{OlsWin} and generalizes the result in \cite{BaeOlsSni}.

math.DS↗
arXiv2012

A local variational principle for random bundle transformations

We introduce local topological entropy $h_{\text{top}}(T, \mathcal{U})$ and two kinds of local measure-theoretic entropy $h_μ^{(r)-}(T,\mathcal{U})$ and $h_μ^{(r)+}(T,\mathcal{U})$ for random bundle transformations. We derive a variational inequality of random local entropy for $h_μ^{(r)+}(T,\mathcal{U})$. As an application of such relation we prove a local variational principle in random dynamical system.

math.DS↗
arXiv2011

Variational Principles For BS Dimension of Subsets

We redefine BS-dimension for Caratheodory structure by packing method. We have the same dimension properties with respect to the cover method and check the Bowen's equation for the new dimension as well. Besides, we consider the relation between the new BS-dimension and upper and lower BS-density respectively. We extend the variational principles of entropy to BS dimension.

math.DS↗
arXiv2010

Topological pressures for $ε$-stable and stable sets

Topological pressures of the preimages of $ε$-stable sets and some certain closed subsets of stable sets in positive entropy systems are investigated. It is showed that the topological pressure of any topological system can be calculated in terms of the topological pressure of the preimages of $ε$-stable sets. For the constructed closed subset of the stable set or the unstable set of any point in a measure-theoretic `rather big' set of a topological system with positive entropy, especially for the weakly mixing subset contained in the closure of stable set and unstable set, it is proved that topological pressures of these subsets can be no less than the measure-theoretic pressure.

math.DS↗
arXiv2010

Projection Pressure and Bowen's Equation for a Class of Self-similar Fractals with Overlap Structure

Let $\{S_i\}_{i=1}^{l}$ be an iterated function system(IFS) on $\mathbb{R}^d$ with attractor K. Let $π$ be the canonical projection. In this paper we define a new concept called "projection pressure" $P_π(ϕ)$ for $ϕ\in C(\mathbb{R}^d)$ 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 $S_i$ 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 $K$.

math.DS↗
arXiv2009

Variational principle for subadditive sequence of potentials in bundle RDS

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

math.DS↗
arXiv2009

Relative local variational principles for subadditive potentials

We prove two relative local variational principles of topological pressure functions $P(T,\mathcal{F},\mathcal{U},y)$ and$P(T,\mathcal{F},\mathcal{U}|Y)$ for a given factor map $π$, an open cover $\mathcal{U} $ and a subadditive sequence of real-valued continuous functions $\mathcal{F}$. By proving the upper semi-continuity and affinity of the entropy maps $h_{\{\cdot\}}(T,\mathcal{U}\mid Y)$ and $h^+_{\{\cdot\}}(T,\mathcal{U}\mid Y)$ on the space of all invariant Borel probability measures, we show that the relative local pressure $P(T,\mathcal{\{\cdot\}},\mathcal{U}|Y)$ for subadditive potentials determines the local measure-theoretic conditional entropies.

math.DS↗