Resonances and Zeta Functions in Smooth Ergodic Theory and Geometry

Deliverables

Open Research Data Pilot (1)

Data Management Plan

The green open access platform WRAP of Warwick makes available the papers accepted for publication in the final (non published) form Moreover, all of the papers of the PI will be posted to the green access platform arXiv

Publications

Peer reviewed articles (5)

The Schottky–Klein prime function and counting functions for Fenchel double crosses

Author(s): Mark Pollicott
Published in: Monatsh. Math, 195, 2021, Page(s) 323–342, ISSN 1436-5081
Publisher: Springer-Verlag
DOI: 10.1007/s00605-021-01547-3

How Many Inflections are There in the Lyapunov Spectrum

Author(s): Oliver Jenkinson; Mark Pollicott; Polina Vytnova
Published in: Comm. Math. Phys., 386, 2021, Page(s) 1383–1411, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04161-4

Effective estimates of Lyapunov exponents for random products of positive matrices

Author(s): Mark Pollicott
Published in: Nonlinearity, 34, 2021, Page(s) 6705–6718, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac15ac

Uniform lower bounds on the dimension of Bernoulli convolutions

Author(s): Victor Kleptsyn; Mark Pollicott; Polina Vytnova
Published in: Advances in Mathematics, 395, 2022, Page(s) 55, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2021.108090

An infinite interval version of the alpha-Kakutani equidistribution problem

Author(s): Mark Pollicott, Ben Sewell
Published in: Israel Journal of Mathematics, 2022, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.48550/arxiv.2103.10235

Book chapters (3)

Statistical properties of the Rauzy-Veech-Zorich map

Author(s): Roman Aimino, Mark Pollicott
Published in: Thermodynamic Formalism, Lecture Notes in Mathematics, 2290, 2021, Page(s) 317-349
Publisher: Springer Verlage
DOI: 10.1007/978-3-030-74863-0_10

Groups, drift and harmonic measures

Author(s): Mark Pollicott, Polina Vytnova
Published in: 2022
Publisher: Springer
DOI: 10.48550/arxiv.2204.08197

Higher Teichmüller theory for surface groups and shifts of finite type

Author(s): Mark Pollicott, Richard Sharp
Published in: Thermodynamic formalism, Lecture Notes in Mathematics, 2290, 2021, Page(s) 395-418
Publisher: Springer Verlag
DOI: 10.1007/978-3-030-74863-0_12

Other (12)

An elementary proof that the Rauzy gasket is fractal

Author(s): Mark Pollicott, Benedict Sewell
Published in: 2022
Publisher: ArXiv

An upper bound on the dimension of the Rauzy gasket

Author(s): Mark Pollicott, Ben Sewell
Published in: 2022
Publisher: ArXiv

Maximizing dimension for Bernoulli measures and the Gauss map

Author(s): Mark Pollicott, Ben Sewell
Published in: Proceedings of the American Mathematical Society, 2023
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2204.07794

Anosov Flows and Dynamical Zeta Functions (Errata)

Author(s): Paolo Giulietti, Carlangelo Liverani, Mark Pollicott
Published in: 2022
Publisher: ArXiv

Minimizing entropy for translation surfaces

Author(s): Paul Colognese, Mark Pollicott
Published in: 2022
Publisher: ArXiv

Hausdorff dimension of Gauss--Cantor sets and two applications to classical Lagrange and Markov spectra

Author(s): Matheus, Carlos; Moreira, Carlos Gustavo; Pollicott, Mark; Vytnova, Polina
Published in: 1, 2020
Publisher: ArXiv
DOI: 10.48550/arxiv.2106.06572

Zeta functions in higher Teichmuller theory

Author(s): Mark Pollicott, Richard Sharp
Published in: 2022
Publisher: ArXiv

Explicit examples of resonances for Anosov maps of the torus

Author(s): Mark Pollicott and Benedict Sewell
Published in: 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2204.01511

Comparison theorems for closed geodesics on negatively curved surfaces

Author(s): Cantrell, Stephen; Pollicott, Mark
Published in: 1, 2020
Publisher: ArXiv

A dynamical approach to validated numerics

Author(s): Oliver Jenkinson, Mark Pollicott
Published in: 2022
Publisher: ArXiv

Accurate bounds on Lyapunov exponents for expanding maps of the interval

Author(s): Mark Pollicott, Polina Vytnova
Published in: 2022
Publisher: ArXiv

The growth and distribution of large circles on translation surfaces

Author(s): Paul Colognese, Mark Pollicott
Published in: 2022
Publisher: ArXiv

Non-peer reviewed articles (3)

Fourier multipliers and transfer operators

Author(s): Mark Pollicott
Published in: J. Fractal Geom, 8, 2021, Page(s) 189–199, ISSN 2308-1309
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jfg/103

Gibbs measures for hyperbolic attractors defined by densities

Author(s): David Parmenter, Mark Pollicott
Published in: Discrete and Continuous Dynamical Systems, 2022, ISSN 1078-0947
Publisher: Dept. of Mathematics, Southwest Missouri State University
DOI: 10.3934/dcds.2022038

Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets

Author(s): Mark Pollicott, Polina Vytnova
Published in: Transactions of the American Mathematical Society, 2022, ISSN 0002-9947
Publisher: American Mathematical Society