相关论文: Multifractal analysis of homological growth rates …
We perform a large deviations analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. For surfaces uniformized by a wide class of Fuchsian groups of the first kind, we prove the existence of the rate function…
We perform a multifractal analysis of the growth rate of the number of cusp windings for the geodesic flow on hyperbolic surfaces with $m \geq 1$ cusps. Our main theorem establishes a conditional variational principle for the Hausdorff…
In this paper, we study the Hausdorff dimension of the generalized intrinsic level set with respect to the given ergodic meausre in a class of non-uniformly hyperbolic interval maps with finitely many branches.
In this paper we investigate the multifractal decomposition of the limit set of a finitely generated, free Fuchsian group with respect to the mean cusp winding number. We will completely determine its multifractal spectrum by means of a…
We study the multifractal analysis of dimension spectrum for almost additive potential in a class of one dimensional non-uniformly hyperbolic dynamic systems and prove that the irregular set has full Hausdroff dimension.
In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the…
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…
Johansson, Jordan, \"Oberg and Pollicott ( Israel J. Math.(2010)) has studied the multifractal analysis of a class of one-dimensional non-uniformly hyperbolic systems, by introducing some new techniques, we extend the results to the case of…
We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of…
On a surface with a Finsler metric, we investigate the asymptotic growth of the number of closed geodesics of length less than $L$ which minimize length among all geodesic multicurves in the same homology class. An important class of…
We propose to study multiple ergodic averages from multifractal analysis point of view. In some special cases in the symbolic dynamics, Hausdorff dimensions of the level sets of multiple ergodic average limit are determined by using Riesz…
Let $f$ be a holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$ of algebraic degree at least $2$ and let $X \subseteq \mathbb{C}\mathbb{P}^k$ be an uniformly expanding set. In this paper, we study multifractal analysis of equilibrium…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
Multifractal analysis studies level sets of asymptotically defined quantities in a topological dynamical system. We consider the topological pressure function on such level sets, relating it both to the pressure on the entire phase space…
For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it…
We survey some results on non-uniform hyperbolicity, geometric pressure and equilibrium states in one-dimensional real and complex dynamics. We present some relations with Hausdorff dimension and measures with refined gauge functions of…
We give an overview of how to construct continued fractions on the Heisenberg group $\mathbb{H}$, the projective and planar Siegel models of the group, and how to perform computations on the group using matrices. We discuss and work with…
A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on the Julia set. We prove the important expanding properties for hyperbolic…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…