Explanipedia

Big Birkhoff sums in $d$-decaying Gauss like iterated function systems Open

Lingmin Liao, Michał Rams · 2021

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Hausdorff and packing dimensions and measures for nonlinear transversally non-conformal thin solenoids Open

Reza Mohammadpour, Feliks Przytycki, Michał Rams · 2021

We extend the results of Hasselblatt and Schmeling [Dimension product structure of hyperbolic sets. Modern Dynamical Systems and Applications . Eds. B. Hasselblatt, M. Brin and Y. Pesin. Cambridge University Press, New York, 2004, pp. 331–…

Spectrum of weighted Birkhoff average Open

Balázs Bárány, Michał Rams, Ruxi Shi · 2021

Let $\{s_n\}_{n\in\N}$ be a decreasing nonsummable sequence of positive reals. In this paper, we investigate the weighted Birkhoff average $\frac{1}{S_n}\sum_{k=0}^{n-1}s_kϕ(T^kx)$ on aperiodic irreducible subshift of finite type $Σ_{\bf A…

Normal sequences with given limits of multiple ergodic averages Open

Lingmin Liao, Michał Rams · 2020

We are interested in the set of normal sequences in the space $\\{0,1\\}^{\\mathbb N}$ with a given frequency of the pattern $11$ in the positions $k$, $2k$. The topological entropy of such sets is determined.

Birkhoff spectrum for piecewise monotone interval maps Open

Thomas Jordan, Michał Rams · 2020

For piecewise monotone interval maps we look at Birkhoff spectra for regular potential functions. This means considering the Hausdorff dimension of the set of points for which the Birkhoff average of the potential takes a fixed value. In t…

Dimension of the repeller for a piecewise expanding affine map Open

Balázs Bárány, Michał Rams, Károly Simon · 2020

In this paper, we study the dimension theory of a class of piecewise affine systems in euclidean spaces suggested by Michael Barnsley, with some applications to the fractal image compression. It is a more general version of the class consi…

The structure of the space of ergodic measures of transitive partially hyperbolic sets Open

Lorenzo J. Díaz, Katrin Gelfert, Tiane Marcarini, Michał Rams · 2019

Normal numbers with given limits of multiple ergodic averages Open

Lingmin Liao, Michał Rams · 2019

We are interested in the set of normal sequences in the space $\{0,1\}^\mathbb{N}$ with a given frequency of the pattern $11$ in the positions $k, 2k$. The topological entropy of such sets is determined.

Metrical Results on the Distribution of Fractional Parts of Powers of Real Numbers Open

Yann Bugeaud, Lingmin Liao, Michał Rams · 2018

We establish several new metrical results on the distribution properties of the sequence ({ x n }) n ≥1 , where {·} denotes the fractional part. Many of them are presented in a more general framework, in which the sequence of functions ( x…

Dimension of generic self-affine sets with holes Open

Henna Koivusalo, Michał Rams · 2018

HAUSDORFF DIMENSION OF THE SET APPROXIMATED BY IRRATIONAL ROTATIONS Open

Dong Han Kim, Michał Rams, Baowei Wang · 2018

Let $\\theta$ be an irrational number and $\\varphi: {\\mathbb N} \\to {\\mathbb\nR}^{+}$ be a monotone decreasing function tending to zero. Let\n$$E_\\varphi(\\theta) =\\Big\\{y \\in \\mathbb R: \\|n\\theta- y\\|<\\varphi(n), \\\n{\\text{…

Nonhyperbolic step skew-products: Entropy spectrum of Lyapunov exponents Open

Lorenzo J. Díaz, Katrin Gelfert, Michał Rams · 2016

We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of $N$, $N\ge2$, symbols and with $C^1$ diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic, exh…

Hausdorff dimension of the set in irrational rotations Open

Dong Han Kim, Michał Rams, Baowei Wang · 2016

Let $\theta$ be an irrational number and $\varphi: {\mathbb N} \to {\mathbb R}^{+}$ be a monotone decreasing function tending to zero. Let $$E_\varphi(\theta) =\Big\{y \in \mathbb R: \|n\theta- y\|<\varphi(n), {\text{for infinitely many}}…

The entropy of Lyapunov-optimizing measures of some matrix cocycles Open

Jairo Bochi, Michał Rams · 2016

We consider one-step cocycles of 2 x 2 matrices, and we are interested in their Lyapunov-optimizing measures, i.e., invariant probability measures that maximize or minimize a Lyapunov exponent. If the cocycle is dominated, that is, the two…

Nonhyperbolic step skew-products: Ergodic approximation Open

Lorenzo J. Díaz, Katrin Gelfert, Michał Rams · 2016

We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperboli…

Dimension maximizing measures and local dimension spectrum for self-affine systems Open

Balázs Bárány, Michał Rams · 2015

In this paper we study the dimension theory of self-affine measures and sets in several aspects. We consider systems satisfying dominated splitting in the linear parts and strong separation condition. The two main results of this paper are…

Dimension of self-affine sets with holes Open

Andrew Ferguson, Thomas Jordan, Michał Rams · 2015

In this paper we compute the dimension of a class of dynamically defined non-conformal sets. Let $X\subseteq\mathbb{T}^2$ denote a Bedford-McMullen set and $T:X\to X$ the natural expanding toral endomorphism which leaves $X$ invariant. For…

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