arXiv subjects

Michal Rams

Publications and source records attributed to Michal Rams.

26 records · Page 2Linked to original sources

arXiv2010

Increasing digit subsystems of infinite iterated function systems

We consider infinite iterated function systems $\{f_i\}_{i=1}^{\infty}$ on $[0,1]$ with a polynomially increasing contraction rate. We look at subsets of such systems where we only allow iterates $f_{i_1}\circ f_{i_2}\circ f_{i_3}\circ...$ if $i_n>Φ(i_{n-1})$ for certain increasing functions $Φ:\mathbb{N}\rightarrow\mathbb{N}$. We compute both the Hausdorff and packing dimensions of such sets. Our results generalize work of Ramharter which shows that the set of continued fractions with strictly increasing digits has Hausdorff dimension 1/2.

math.DS↗

arXiv2010

Lyapunov spectrum for rational maps

We study the dimension spectrum of Lyapunov exponents for rational maps on the Riemann sphere.

math.DS↗

arXiv2010

On some non-conformal fractals

This paper presents a simple method of calculating the Hausdorff dimension for a class of non-conformal fractals.

math.DS↗

arXiv2009

Multifractal analysis for Bedford-McMullen carpets

In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where the multifractal analysis is computed with strong additional separation assumptions.

math.DS↗

arXiv2009

Multifractal analysis of weak Gibbs measures for non-uniformly expanding C^1 maps

We consider the local dimension spectrum of a weak Gibbs measure on a C^1 non-uniformly hyperbolic system of Manneville- Pomeau type. We present the spectrum in three ways: using invariant measures, uniformly hyperbolic ergodic measures and equilibrium states. We are also proving analyticity of the spectrum under additional assumptions. All three presentations are well known for smooth uniformly hyperbolic systems.

math.DS↗

arXiv2008

On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS

We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.

math.DS↗

arXiv2007

The Lyapunov spectrum of some parabolic systems

We study the Hausdorff dimension spectrum for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given lower and upper Lyapunov exponents and, in particular, with zero lower Lyapunov exponent. We prove that the level set of points with zero exponent has full Hausdorff dimension, but carries no topological entropy.

math.DS↗

arXiv2007

Growth rates for geometric complexities and counting functions in polygonal billiards

We introduce a new method for estimating the growth of various quantities arising in dynamical systems. We apply our method to polygonal billiards on surfaces of constant curvature. For instance, we obtain power bounds of degree two plus epsilon in length for the number of billiard orbits between almost all pairs of points in a planar polygon.

math.DS↗