相关论文: Symbolic dynamics in mean dimension theory

We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise…

Let $\Theta=\{\theta_n\}, \Lambda=\{\lambda_n\}$ be two sequences of independent and identically distributed uniform random variables on $[0,1]$. The random vector-valued Weierstrass function is given by \[ f_{\Theta,\Lambda}(t)= \left(…

For a hyperbolic map f on a saddle type fractal Lambda with self-intersections, the number of f- preimages of a point x in Lambda may depend on x. This makes estimates of the stable dimensions more difficult than for diffeomorphisms or for…

Statistical entropies of a general relativistic ideal gas obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are calculated in a general axisymmetry space-time of arbitrary dimension. This general formation can be used to…

In this paper, we will introduce and study the lower moving digit mean $\underline{M}(x)$ and the upper moving digit mean $\overline{M}(x)$ of $x\in[0,1]$ in $p$-adic expansion, where $p\geq2$ is an integer. Moreover, the Hausdorff…

The description of a closed quantum system is extended with the identification of an underlying substructure enabling an expanded formulation of dynamics in the Heisenberg picture. Between measurements a ``state point" moves in an…

Time averaging over the trajectory of a wavepacket up to time T defines a statistical operator (density matrix). The corresponding (Von Neumann) entropy is proven to asymptotically increase with time like D.log T, with D the Hausdorff…

We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof…

Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression but the results we obtained can be…

In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of…

In this paper, we investigate the Hausdorff measure of shrinking target sets in $\beta$-dynamical systems. These sets are dynamically defined in analogy to the classical theory of weighted and multiplicative approximation. While the…

We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a new, unified approach to various celebrated theorems about…

Wasserstein distortion is a one-parameter family of distortion measures that was recently proposed to unify fidelity and realism constraints. After establishing continuity results for Wasserstein in the extreme cases of pure fidelity and…

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is…

As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension three, we introduce a $C^2$-open set of diffeomorphisms of $\mathbb R^3$ having two horseshoes with different dimensions of instability. We prove…

The Jarn\'ik-Besicovitch theorem is a fundamental result in metric number theory which gives the Hausdorff dimension for limsup sets. We investigate a related problem of estimating the Hausdorff dimension of a liminf set. Let $h>0, \tau\geq…

Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for the sample functions of a large class of self-affine random…

We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some partially hyperbolic systems and geometric Lorenz flows. We…

We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in Z^d. This endeavor solves a problem of Barlow and Taylor (1991).

Subspace representation is a fundamental technique in various fields of machine learning. Analyzing a geometrical relationship among multiple subspaces is essential for understanding subspace series' temporal and/or spatial dynamics. This…