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Resonances and Zeta Functions in Smooth Ergodic Theory and Geometry

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Open Research Data Pilot (1)
Data Management Plan (opens in new window)

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 (16)
The Schottky–Klein prime function and counting functions for Fenchel double crosses (opens in new window)

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

An elementary proof that the Rauzy gasket is fractal (opens in new window)

Author(s): Mark Pollicott, Benedict Sewell
Published in: Communications in Mathematical Physics, Issue 1, 2023, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2023.66

How Many Inflections are There in the Lyapunov Spectrum (opens in new window)

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

Extreme events for horocycle flows (opens in new window)

Author(s): Jens Marklof, Mark Pollicott
Published in: Nonlinearity, Issue 38, 2025, Page(s) 055003, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/adc8f0

Accurate bounds on Lyapunov exponents for expanding maps of the interval

Author(s): Mark Pollicott, Polina Vytnova
Published in: Communications in Mathematical Physics, Issue 3, 2022, ISSN 0010-3616
Publisher: Springer Verlag

Effective estimates of Lyapunov exponents for random products of positive matrices (opens in new window)

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

Comparison theorems for closed geodesics on negatively curved surfaces

Author(s): Cantrell, Stephen; Pollicott, Mark
Published in: Groups Geom. Dyn., Issue 1, 2020, ISSN 1661-7207
Publisher: European Mathematical Society Publishing House

Rapid mixing for compact group extensions of hyperbolic flows (opens in new window)

Author(s): Mark Pollicott, Daofei Zhang
Published in: Transactions of the American Mathematical Society, 2025, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/9424

Zeta functions in higher Teichmuller theory (opens in new window)

Author(s): Mark Pollicott, Richard Sharp
Published in: Mathematische Zeitschrift, Issue 1, 2024, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-024-03437-4

Uniform lower bounds on the dimension of Bernoulli convolutions (opens in new window)

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

Maximizing dimension for Bernoulli measures and the Gauss map (opens in new window)

Author(s): Mark Pollicott
Published in: Proceedings of the American Mathematical Society, 2025, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/15310

Zeta functions in higher Teichmüller theory (opens in new window)

Author(s): Mark Pollicott, Richard Sharp
Published in: Mathematische Zeitschrift, Issue 306, 2024, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-024-03437-4

An infinite interval version of the alpha-Kakutani equidistribution problem (opens in new window)

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

Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map (opens in new window)

Author(s): Mark Pollicott, Julia Slipantschuk
Published in: Nonlinearity, Issue 37, 2024, Page(s) 095013, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad6053

Rigidity of pressures of Hölder potentials and the fitting of analytic functions through them (opens in new window)

Author(s): LIANGANG MA; MARK POLLICOTT
Published in: Crossref, Issue 1, 2024, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2024.9

An infinite interval version of the {\alpha}-Kakutani equidistribution problem (opens in new window)

Author(s): Pollicott, Mark; Sewell, Benedict
Published in: Israel Journal of Mathematics, Issue 1, 2023, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-023-2569-6

Book chapters (5)
Statistical properties of the Rauzy-Veech-Zorich map (opens in new window)

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

A dynamical approach to validated numerics

Author(s): Jenkinson, Oliver; Pollicott, Mark
Published in: )A vision for dynamics in the 21st century—the legacy of Anatole Katok, 2024, Page(s) 168–206, ISBN 978-1-009-27890-4
Publisher: Cambridge University Press

A dynamical approach to validated numerics

Author(s): Oliver Jenkinson, Mark Pollicott
Published in: Issue 4, 2024
Publisher: Cambridge University Press

Groups, drift and harmonic measures (opens in new window)

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 (opens in new window)

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

Other (23)
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 (opens in new window)

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

An ergodic approach towards an equidistribution result of Ferrero--Washington (opens in new window)

Author(s): Lee, Jungwon; Palvannan, Bharathwaj
Published in: Issue 3, 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2207.09620

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 (opens in new window)

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

Zeta functions in higher Teichmuller theory (opens in new window)

Author(s): Pollicott,Mark, Sharp, Richard
Published in: 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2203.15741

Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map (opens in new window)

Author(s): Pollicott, Mark; Slipantschuk, Julia
Published in: Issue 1, 2023, ISSN 1661-7207
Publisher: ArXiv
DOI: 10.48550/arxiv.2308.04293

Euclidean algorithms are Gaussian over imaginary quadratic fields (opens in new window)

Author(s): Kim, Dohyeong; Lee, Jungwon; Lim, Seonhee
Published in: Issue 3, 2024
Publisher: ArXiv
DOI: 10.48550/arxiv.2401.00734

Explicit examples of resonances for Anosov maps of the torus (opens in new window)

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: Issue 1, 2020
Publisher: ArXiv

Rigidity of pressures of Hölder potentials and the fitting of analytic functions via them (opens in new window)

Author(s): Ma, Liangang; Pollicott, Mark
Published in: Rigidity of pressures of Hölder potentials and the fitting of analytic functions via them, Issue 1, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2210.16794

Sierpiński Fractals and the Dimension of Their Laplacian Spectrum (opens in new window)

Author(s): Mark Pollicott; Julia Slipantschuk
Published in: Mathematical and Computational Applications, Vol 28, Iss 3, p 70 (2023), Issue 1, 2023
Publisher: ArXiv
DOI: 10.3390/mca28030070

Constructing equilibrium states for some partially hyperbolic attractors via densities (opens in new window)

Author(s): Parmenter, David; Pollicott, Mark
Published in: Issue 3, 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2210.10701

Continuous eigenfunctions of the transfer operator for the Dyson model (opens in new window)

Author(s): Johansson, Anders; Öberg, Anders; Pollicott, Mark
Published in: Issue 3, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2304.04202

The growth and distribution of large circles on translation surfaces

Author(s): Paul Colognese, Mark Pollicott
Published in: Issue 3, 2021
Publisher: ArXiv

"Sierpiński Fractals and the Dimension of Their Laplacian Spectrum"

Author(s): Slipantschuk, Mark Pollicott; Julia
Published in: Mathematical and Computational Applications; Volume 28; Issue 3; Pages: 70, Issue 3, 2023
Publisher: ArXiv

A dynamical approach to validated numerics

Author(s): Oliver Jenkinson, Mark Pollicott
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

EDMD for expanding circle maps and their complex perturbations (opens in new window)

Author(s): Bandtlow, Oscar F.; Just, Wolfram; Slipantschuk, Julia
Published in: Issue 1, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2308.01467

Complex Continued Fractions and Extremal Theory (opens in new window)

Author(s): Baumgartner, Alexander; Pollicott, Mark
Published in: Issue 1, 2024
Publisher: ArXiv
DOI: 10.48550/arxiv.2401.00626

Resonances for rational Anosov maps on the torus (opens in new window)

Author(s): Slipantschuk, Julia; Bandtlow, Oscar F.; Just, Wolfram
Published in: Issue 3, 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2211.05925

Non-peer reviewed articles (7)
An upper bound on the dimension of the Rauzy gasket

Author(s): Mark Pollicott, Ben Sewell
Published in: Bull. Soc. Math. France, Issue 3, 2023, ISSN 0037-9484
Publisher: Societe Mathematique de France

Fourier multipliers and transfer operators (opens in new window)

Author(s): Mark Pollicott
Published in: J. Fractal Geom, Issue 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 (opens in new window)

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

Accurate bounds on Lyapunov exponents for expanding maps of the interval (opens in new window)

Author(s): Mark Pollicott, Polina Vytnova
Published in: Communications in Mathematical Physics, Issue 4, 2023, Page(s) 485–502, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.48550/arxiv.2201.04752

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

Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups (opens in new window)

Author(s): M. Pollicott, P. Vytnova
Published in: Transactions of the American Mathematical Society, Series B, Issue 9, 2023, Page(s) 1102-1159, ISSN 2330-0000
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/btran/109

Minimizing entropy for translation surfaces

Author(s): Paul Colognese, Mark Pollicott
Published in: Conformual Geomety and Dynamics, Issue 3, 2022, ISSN 1088-4173
Publisher: American Mathematical Society

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Last update: 17 February 2025

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