5 papers
On fast Lyapunov spectra for Markov-Rényi maps
Lulu Fang, Carlos Gustavo Moreira, Zhichao Wang +1
In this paper, we study the multifractal analysis for Markov-Rényi maps, which form a canonical class of piecewise differentiable interval maps, with countably many branches and ma…
Topological entropy and Hausdorff dimension of shrinking target sets
Xiaobo Hou, Xueting Tian, Yiwei Zhang
In this paper, we study the topological entropy and the Hausdorff dimension of a shrinking target set. We give lower and upper bounds of topological entropy and Hausdorff dimension…
Graphs of continuous but non-affine functions are never self-similar
Carlos Gustavo Moreira, Jinghua Xi, Yiwei Zhang
Bandt and Kravchenko \cite{BandtKravchenko2010} proved that if a self-similar set spans , then there is no tangent hyperplane at any point of the set. In particular, this ind…
Fractal geometry of continued fractions with large coefficients and dimension drop problems
Lulu Fang, Carlos Gustavo Moreira, Yiwei Zhang
In 1928, Jarn\'ık \cite{Jar} obtained that the set of continued fractions with bounded coefficients has Hausdorff dimension one. Good \cite{Goo} observed a dimension drop phenomeno…
On shrinking targets for linear expanding and hyperbolic toral endomorphisms
Zhang-nan Hu, Tomas Persson, Wanlou Wu +1
Let be an invertible matrix with integer elements. Then determines a self-map of the -dimensional torus . Given a…