3 citations · 8 across the 9 of their papers we have counts for
10 papers
Hausdorff dimension of the Apollonian gasket
Polina Vytnova, Caroline Wormell
The Apollonian gasket is a well-studied circle packing. Important properties of the packing, including the distribution of the circle radii, are governed by its Hausdorff dimension…
On the graph of the dimension function of the Lagrange and Markov spectra
Carlos Matheus, Carlos Gustavo Moreira, Polina Vytnova
We study the graph of the function encoding the Hausdorff dimensions of the classical Lagrange and Markov spectra with half-infinite lines of the form . For th…
Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces
Mark Pollicott, Polina Vytnova
In the present paper we give a simple mathematical foundation for describing the zeros of the Selberg zeta functions for certain very symmetric infinite area surfaces . Fo…
Groups, drift and harmonic measures
Mark Pollicott, Polina Vytnova
In this short note we will describe an old problem and a new approach which casts light upon it. The old problem is to understand the nature of harmonic measures for cocompact Fuch…
The Bowen$\unicode{x2013}$Series coding and zeros of zeta functions
Mark Pollicott, Polina Vytnova
We give a discussion of the classical Bowen$\unicode{x2013}$Series coding and, in particular, its application to the study of zeta functions associated to geodesic flows and their…
Accurate bounds on Lyapunov exponents for expanding maps of the interval
Mark Pollicott, Polina Vytnova
In this short note we describe a simple but remarkably effective method for rigorously estimating Lyapunov exponents for expanding maps of the interval. We illustrate the applicabi…
Hausdorff dimension of Gauss--Cantor sets and two applications to classical Lagrange and Markov spectra
Carlos Matheus, Carlos Gustavo Moreira, Mark Pollicott +1
This paper is dedicated to the study of two famous subsets of the real line, namely Lagrange spectrum and Markov spectrum . Our first result, Theorem 2.1, provides a rigorou…
Uniform lower bounds on the dimension of Bernoulli convolutions
Victor Kleptsyn, Mark Pollicott, Polina Vytnova
In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the b…
Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups
Mark Pollicott, Polina Vytnova
In this note we will describe a simple and practical approach to get rigorous bounds on the Hausdorff dimension of limits sets for some one dimensional Markov iterated function sch…
How many inflections are there in the Lyapunov spectrum?
Oliver Jenkinson, Mark Pollicott, Polina Vytnova
Iommi & Kiwi showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this pape…