2023

Pollicott, Mark and Sewell, Benedict (2023) Explicit examples of resonances for Anosov maps of the torus. Nonlinearity, 36 (1). pp. 110-132. doi:10.1088/1361-6544/ac9a2e ISSN 0951-7715.

2022

Matheus, Carlos, Moreira, Carlos Gustavo, Pollicott, Mark and Vytnova, Polina (2022) Hausdorff dimension of Gauss–Cantor sets and two applications to classical Lagrange and Markov spectra. Advances in Mathematics, 409 (Pt B). 108693. doi:10.1016/j.aim.2022.108693 ISSN 0001-8708.

Pollicott, Mark and Vytnova, Polina (2022) Accurate bounds on Lyapunov exponents for expanding maps of the interval. Communications in Mathematical Physics . doi:10.1007/s00220-022-04495-7 ISSN 0010-3616. (In Press)

Pollicott, Mark and Cantrell, Stephen (2022) Comparison theorems for closed geodesics on negatively curved surfaces. Groups, Geometry and Dynamics, 16 (2). pp. 461-491. doi:10.4171/ggd/671 ISSN 1661-7207.

Parmenter, David and Pollicott, Mark (2022) Gibbs measures for hyperbolic attractors defined by densities. Discrete and Continuous Dynamical Systems. Series A, 42 (8). pp. 3953-3977. doi:10.3934/dcds.2022038 ISSN 1078-0947.

Kleptsyn, V., Pollicott, Mark and Vytnova, Polina (2022) Uniform lower bounds on the dimension of Bernoulli convolutions. Advances in Mathematics, 395 . 108090. doi:10.1016/j.aim.2021.108090 ISSN 0001-8708.

Pollicott, Mark and Vytnova, Polina (2022) Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups. Transactions of the American Mathematical Society . ISSN 0002-9947. (In Press)

Pollicott, Mark (2022) Maximizing measures for Bernoulli measures and the Gauss map. Proceedings of the American Mathematical Society . ISSN 0002-9939. (In Press)

Colognese, Paul and Pollicott, Mark (2022) Minimizing entropy for translation surfaces. Conformal Geometry and Dynamics, 26 (6). pp. 97-110. doi:10.1090/ecgd/374 ISSN 1088-4173.

2021

Pollicott, Mark (2021) Effective estimates of Lyapunov exponents for random products of positive matrices. Nonlinearity, 34 (10). pp. 6705-6718. doi:10.1088/1361-6544/ac15ac ISSN 1361-6544.

Jenkinson, O., Pollicott, Mark and Vytnova, Polina (2021) How many inflections are there in the Lyapunov spectrum? Communications in Mathematical Physics, 386 (3). pp. 1383-1411. doi:10.1007/s00220-021-04161-4 ISSN 0010-3616.

Pollicott, Mark and Urbanski, Mariuski (2021) Asymptotic counting in conformal dynamical systems. Memoirs of the American Mathematical Society, 271 (1327). doi:10.1090/memo/1327 ISSN 0065-9266.

Pollicott, Mark (2021) The Schottky–Klein prime function and counting functions for Fenchel double crosses. Monatshefte fur Mathematik, 195 (2). pp. 323-342. doi:10.1007/s00605-021-01547-3 ISSN 0026-9255.

Pollicott, Mark (2021) Fourier multipliers and transfer operators. Journal of Fractal Geometry, 8 (2). pp. 189-199. doi:10.4171/jfg/103 ISSN 2308-1309.

Pollicott, Mark and Sharp, Richard (2021) Higher Teichmüller theory for surface groups and shifts of finite type. In: Pollicott, M. and Vaienti, S., (eds.) Thermodynamic Formalism. Lecture Notes in Mathematics, 2290 . Cham: Springer, pp. 395-418. ISBN 9783030748623

Aimino, Romain and Pollicott, Mark (2021) Statistical properties of the Rauzy-Veech-Zorich map. In: Thermodynamic Formalism. Lecture Notes in Mathematics, 2290 . Cham: Springer, pp. 317-349. ISBN 9783030748623

2020

Pollicott, Mark (2020) Dynamical zeta functions and the distribution of orbits. In: Ji, Lizhen and Papadopoulos, Athanase and Yau, Shing-Tung, (eds.) Handbook of Group Actions V. Advanced Lectures in Mathematics, 48 (V). Massachusetts : International Press of Boston. ISBN 9781571463906

Jenkinson, Oliver and Pollicott, Mark (2020) Rigorous dimension estimates for Cantor sets arising in Zaremba theory. In: Moree, Pieter and Pohl, Anke and Snoha, L’ubomír and Ward, Tom, (eds.) Dynamics : topology and numbers. Contemporary Mathematics, 744 . Providence, Rhode Island: American Mathematical Society, pp. 83-107. ISBN 9781470451004

Colognese, Paul and Pollicott, Mark (2020) Volume growth for infinite graphs and translation surfaces. In: Moree, Pieter and Pohl, Anke and Snoha, L’ubomír and Ward, Tom, (eds.) Dynamics : topology and numbers. Contemporary Mathematics, 744 . Providence, Rhode Island: American Mathematical Society. ISBN 9781470451004

2019

Pollicott, Mark and Vytnova, Polina (2019) Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces. Geometriae Dedicata, 201 . pp. 155-186. doi:10.1007/s10711-018-0386-6 ISSN 0046-5755.

Johansson, Anders, Oberg, Anders and Pollicott, Mark (2019) Phase transitions in long-range Ising models and an optimal condition for factors of g-measures. Ergodic Theory and Dynamical Systems, 39 (5). pp. 1317-1330. doi:10.1017/etds.2017.66 ISSN 0143-3857.

2018

Jenkinson, Oliver and Pollicott, Mark (2018) Joint spectral radius, Sturmian measures and the finiteness conjecture. Ergodic Theory and Dynamical Systems, 38 (8). pp. 3062-3100. doi:10.1017/etds.2017.18 ISSN 0143-3857.

Pollicott, Mark (2018) Appolonius circle counting. LMS Newsletter, 478 . ISSN 2516-3841.

Cipriano, Italo Umberto and Pollicott, Mark (2018) Stationary measures associated to analytic iterated function schemes. Mathematische Nachrichten, 291 (7). pp. 1049-1054. doi:10.1002/mana.201600127 ISSN 0025-584X.

Pollicott, Mark and Jenkinson, Oliver (2018) Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets : a hundred decimal digits for the dimension of E2. Advances in Mathematics, 325 . pp. 87-115. doi:10.1016/j.aim.2017.11.028 ISSN 0001-8708.

Pollicott, Mark, Jenkinson, Oliver and Vytnova, Polina (2018) Rigorous computation of diffusion coefficients for expanding maps. Journal of Statistical Physics, 170 (2). pp. 221-253. doi:10.1007/s10955-017-1930-8 ISSN 0022-4715.

Pollicott, Mark (2018) Hyperbolic systems, zeta functions and other friends. Dynamical Systems : Simons Semester in Banach Center, 2015, 115 . pp. 145-182. doi:10.4064/bc115-5

2017

Pollicott, Mark and Vytnova, Polina (2017) Critical points for the Hausdorff Dimension of pairs of pants. Groups, Geometry and Dynamics, 11 (4). pp. 1497-1519. doi:10.4171/GGD/436 ISSN 1661-7207.

Pollicott, Mark (2017) Amenable covers for surfaces and growth of closed geodesics. Advances in Mathematics, 319 . pp. 599-609. doi:10.1016/j.aim.2017.08.020 ISSN 0001-8708.

Pollicott, Mark and Urbanski, Mariuski (2017) Open conformal systems and perturbations of transfer operators. Lecture Notes in Mathematics . Cham : Springer International Publishing AG. ISBN 9783319721798

Galatolo, Stefano and Pollicott, Mark (2017) Controlling the statistical properties of expanding maps. Nonlinearity, 30 . 2737. ISSN 0951-7715.

Pollicott, Mark (2017) A note on the shrinking sector problem for surfaces of variable negative curvature. Steklov Institute of Mathematics. Proceedings, 297 (1). pp. 254-263. ISSN 0081-5438.

Pollicott, Mark (2017) A nonlinear transfer operator theorem. Journal of Statistical Physics, 166 (3). pp. 516-524. doi:10.1007/s10955-016-1646-1 ISSN 0022-4715.

Pollicott, Mark and Urbański, Mariusz (2017) Applications : Escape Rates for Multimodal Maps and One-Dimensional Complex Dynamics. In: Open Conformal Systems and Perturbations of Transfer Operators. Cham Springer, pp. 147-187. ISBN 9783319721781

Pollicott, Mark and Urbański, Mariusz (2017) Escape Rates for Conformal GDMSs and IFSs. In: Open Conformal Systems and Perturbations of Transfer Operators. Cham Springer, pp. 87-145. ISBN 9783319721781

Pollicott, Mark and Urbański, Mariusz (2017) The Keller-Liverani Perturbation Theorem. In: Open Conformal Systems and Perturbations of Transfer Operators. Lecture Notes in Mathematics, 2206 . Cham Springer, 189-193 .

Pollicott, Mark and Urbański, Mariusz (2017) Singular Perturbations of Classical Original Perron–Frobenius Operators on Countable Alphabet Symbol Spaces. In: Open Conformal Systems and Perturbations of Transfer Operators. Cham Springer, pp. 19-51. ISBN 9783319721781

Pollicott, Mark and Urbański, Mariusz (2017) Symbol Escape Rates and the Survivor Set K(Un). In: Open Conformal Systems and Perturbations of Transfer Operators. Cham Springer, pp. 53-85. ISBN 9783319721781

2016

Pollicott, Mark and Vytnova, Polina (2016) Linear response and periodic points. Nonlinearity, 29 (10). ISSN 0951-7715.

Pollicott, Mark and Sharp, Richard (2016) Weil–Petersson metrics, Manhattan curves and Hausdorff dimension. Mathematische Zeitschrift, 282 (3-4). pp. 1007-1016. doi:10.1007/s00209-015-1575-8 ISSN 0025-5874.

2015

Kagiso, Dintle Nelson and Pollicott, Mark (2015) Computing multifractal spectra. Dynamical Systems, 30 (4). pp. 404-425. doi:10.1080/14689367.2015.1062977 ISSN 1468-9367.

Pollicott, Mark and Vytnova, Polina (2015) Estimating singularity dimension. Mathematical Proceedings of the Cambridge Philosophical Society, 158 (2). pp. 223-238. doi:10.1017/S030500411400053X ISSN 0305-0041.

Pollicott, M. (2015) Analyticity of dimensions for hyperbolic surface diffeomorphisms. Proceedings of the American Mathematical Society, 143 (8). pp. 3465-3474. doi:10.1090/proc/12477 ISSN 0002-9939.

Paulin, Frédéric, Pollicott, Mark and Schapira, Barbara (2015) Equilibrium states in negative curvature. Asterisque, 373 . doi:10.24033/ast.975 ISSN 0303-1179.

2014

Pollicott, Mark and Sharp, Richard (2014) A Weil–Petersson type metric on spaces of metric graphs. Geometriae Dedicata, Volume 172 (Number 1). pp. 229-244. doi:10.1007/s10711-013-9918-2 ISSN 0046-5755.

Pollicott, Mark and Felton, Philip (2014) Estimating Mahler measures using periodic points for the doubling map. Indagationes Mathematicae, Volume 25 (Number 4). pp. 619-631. doi:10.1016/j.indag.2014.04.002 ISSN 00193577.

Pollicott, Mark (2014) Zeta function for Anosov Flows. In: International Congress of Mathematicians (ICM 2014), Korea, 13-21 Aug 2014. Published in: Proceedings of the International Congress of Mathematicians : Seoul 2014, 3 pp. 661-681. ISBN 9788961058032 .

2013

Giulietti, Paolo, Liverani, Carlangelo and Pollicott, Mark (2013) Anosov flows and dynamical Zeta functions. Annals of Mathematics, 178 (2). 687-773 . doi:10.4007/annals.2013.178.2.6 ISSN 0003-486X.

Pollicott, Mark and Sharp, Richard (2013) Correlations of length spectra for negatively curved manifolds. Communications in Mathematical Physics, Volume 319 (Number 2). pp. 515-533. doi:10.1007/s00220-012-1644-3 ISSN 0010-3616.

Magalhães, M. L. S. and Pollicott, Mark (2013) Geometry and dynamics of planar linkages. Communications in Mathematical Physics, Volume 317 (Number 3). pp. 615-634. doi:10.1007/s00220-012-1521-0 ISSN 0010-3616.

2012

Pollicott, Mark and Sharp, Richard (2012) Ergodic theorems for actions of hyperbolic groups. Proceedings of the American Mathematical Society, 141 (5). pp. 1749-1757. doi:10.1090/S0002-9939-2012-11447-9 ISSN 0002-9939.

Ferguson, Andrew and Pollicott, Mark (2012) Escape rates for Gibbs measures. Ergodic Theory and Dynamical Systems, Volume 32 (Number 3). pp. 961-988. doi:10.1017/S0143385711000058 ISSN 0143-3857.

Pollicott, Mark, Wang, Hao and Weiss, Howard (2012) Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem. Journal of Biological Dynamics, Vol.6 (No.2). pp. 509-523. doi:10.1080/17513758.2011.645510 ISSN 1751-3758.

Bárány, B., Pollicott, Mark and Simon, K. (2012) Stationary measures for projective transformations : the Blackwell and Furstenberg measures. Journal of Statistical Physics, Vol.148 (No.3). pp. 393-421. doi:10.1007/s10955-012-0541-7 ISSN 0022-4715.

Johannson, Anders, Öberg, Anders and Pollicott, Mark (2012) Unique Bernoulli g-measures. Journal of the European Mathematical Society, Vol.14 (No.5). pp. 1599-1615. doi:10.4171/JEMS/342 ISSN 1435-9855.

Pollicott, Mark (2012) A note on the growth of periodic points for commuting toral automorphisms. ISRN Geometry, Vol.2012 . Article no. 165808. doi:10.5402/2012/165808 ISSN 2090-6315.

2011

Pollicott, Mark (2011) Computing entropy rates for hidden Markov processes. In: Marcus, Brian and Petersen, Karl and Weissman, Tsachy, (eds.) Entropy of hidden Markov processes and connections to dynamical systems : papers from the Banff International Research Station workshop. London Mathematical Society lecture note series . Cambridge, UK ; New York : Cambridge University Press, pp. 223-245. ISBN 9780521111133

Pollicott, Mark and Kempton, Thomas (2011) Factors of Gibbs measures for full shifts. In: Marcus, Brian and Petersen, Karl and Weissman, Tsachy, (eds.) Entropy of hidden Markov processes and connections to dynamical systems : papers from the Banff International Research Station workshop. London Mathematical Society lecture note series . Cambridge, UK ; New York : Cambridge University Press, pp. 246-257. ISBN 9780521111133

Pollicott, Mark and Sharp, Richard (2011) On the Hannay–Ozorio De Almeida sum formula. In: Peixoto, Mauricio Matos and Pinto, Alberto Adrego and Rand, D. A. (David A.), (eds.) Dynamics, Games and Science II. Springer Proceedings in Mathematics, Vol.2 . Berlin ; Heidelberg: Springer, pp. 575-590. ISBN 9783642147876

2010

Pollicott, Mark (2010) Maximal Lyapunov exponents for random matrix products. Inventiones Mathematicae, Vol.181 (No.1). pp. 209-226. doi:10.1007/s00222-010-0246-y ISSN 0020-9910.

Johansson, Anders, Jordan, Thomas M., Oberg, Anders and Pollicott, Mark (2010) Multifractal analysis of non-uniformly hyperbolic systems. Israel Journal of Mathematics, Vol.177 (No.1). pp. 125-144. doi:10.1007/s11856-010-0040-y ISSN 0021-2172.

Pollicott, Mark, Weiss, Howard and Wolpert, Scott A. (2010) Topological dynamics of the Weil–Petersson geodesic flow. Advances in Mathematics, Vol.223 (No.4). pp. 1225-1235. doi:10.1016/j.aim.2009.09.011 ISSN 0001-8708.

Pollicott, Mark (2010) Asymptotic vertex growth for graphs. In: Workshop on Spectrum and Dynamics, Ctr Rech Math, Montreal, Canada, April 07-11, 2008. Published in: Spectrum and Dynamics: Proceedings of the Workshop Held in Montreal, QC, April 7-11, 2008, Vol.52 pp. 137-145. ISBN 978-0-8218-4778-7.

Pollicott, Mark (2010) Dynamical zeta functions. Integers : electronic journal of combinatorial number theory, Vol.11B . Article no. A11. ISSN 1553-1732.

Pollicott, Mark (2010) Rates of convergence for linear actions of cocompact lattices on the complex plane. Integers : electronic journal of combinatorial number theory, Vol.11B . Article no. A12. ISSN 1553-1732.

Pollicott, Mark and Sharp, Richard (2010) Statistics of matrix products in hyperbolic geometry. In: International Conference on Dynamical Numbers: Interplay Between Dynamical systems and Number Theory, Max Planck Inst, Bonn, Germany, 20-24 Jun 2009 . Published in: Dynamical Numbers: Interplay Between Dynamical Systems and Number Theory , Volume 532 pp. 213-230. ISSN 0271-4132.

2009

Pollicott, Mark and Weiss, Howard (2009) Ergodicity of the geodesic flow on non-complete negatively curved surfaces. Asian Journal of Mathematics, Vol.13 (No.3). pp. 405-419. ISSN 1093-6106.

Pollicott, Mark and Sharp, Richard (2009) Large deviations for intermittent maps. Nonlinearity, Vol.22 (No.9). pp. 2079-2092. doi:10.1088/0951-7715/22/9/001 ISSN 0951-7715.

Pollicott, Mark and Sharp, Richard (2009) Large deviations, fluctuations and shrinking intervals. Communications in Mathematical Physics, Vol.290 (No.1). pp. 321-334. doi:10.1007/s00220-008-0725-9 ISSN 0010-3616.

Pollicott, Mark (2009) Limiting distributions for geodesics excursions on the modular surface. In: International Conference on Spectral Analysis in Gerometry and Number Theory held in Honor of Toshikazu Sunada, Nagoya Univ, Nagoya, Japan, August 06-10, 2007. Published in: Contemporary Mathematics, Vol.484 pp. 177-185. ISBN 978-0-8218-4269-0. doi:10.1090/conm/484 ISSN 0271-4132.

Pollicott, Mark (2009) Normal points for generic hyperbolic maps. In: International Conference on Dynamical Systems held in honor of Michal Misurewicz, Polish Acad Sci, Inst Math, Bedlewo, Poland, 2008. Published in: Fundamenta Mathematicae, Vol.206 pp. 271-280. doi:10.4064/fm206-0-15 ISSN 0016-2736.

Jordan, Thomas, Kesseboehmer, Marc, Pollicott, Mark and Stratmann, Bernd O. (2009) Sets of nondifferentiability for conjugacies between expanding interval maps. In: International Conference on Dynamical Systems held in honor of Michal Misurewicz, Polish Acad Sci, Inst Math, Bedlewo, Poland, 2008. Published in: Fundamenta Mathematicae, Vol.206 pp. 161-183. doi:10.4064/fm206-0-10 ISSN 0016-2736.

2008

Jordan, T. (Thomas) and Pollicott, Mark (2008) The Hausdorff dimension of measures for iterated function systems which contract on average. Discrete and Continuous Dynamical Systems, Vol.22 (No.1-2). pp. 235-246. doi:10.3934/dcds.2008.22.235 ISSN 1078-0947.

Pollicott, Mark and Weiss, Howard (2008) How smooth is your wavelet? Wavelet regularity via thermodynamic formalism. Communications in Mathematical Physics, Volume 281 (Number 1). pp. 1-21. doi:10.1007/s00220-008-0457-x ISSN 0010-3616.

Pollicott, Mark and Sharp, Richard (2008) Addendum: an analogue of Artin reciprocity for closed orbits of skew products. Ergodic Theory and Dynamical Systems, Vol.28 (No.2). pp. 547-552. doi:10.1017/S0143385707000569 ISSN 0143-3857.

Parry, William and Pollicott, Mark (2008) An analogue of Bauer’s theorem for closed orbits of skew products. Ergodic Theory and Dynamical Systems, Vol.28 (No.2). pp. 535-546. doi:10.1017/S0143385707000557 ISSN 0143-3857.

Pollicott, Mark, Sharp, Richard, Tuncel, S. and Walters, Peter (2008) The mathematical research of William Parry FRS. Ergodic Theory and Dynamical Systems, Vol.28 (No.2). pp. 321-337. doi:10.1017/S0143385708000102 ISSN 0143-3857.

Burns, Keith, Dolgopyat, Dmitry, Pesin, Yakov and Pollicott, Mark (2008) Stable ergodicity for partially hyperbolic attractors with negative central exponents. Journal of Modern Dynamics, Vol.2 (No.1). pp. 63-81. ISSN 1930-5311.

Pollicott, Mark and Sharp, Richard (2008) Periodic orbits and holonomy for hyperbolic flows. In: Workshop on Dynamical Systems and Related Topics, Univ Maryland, College Pk, MD, Mar 15-18, 2008. Published in: Contemporary Mathematics, Volume 469 pp. 289-302. ISBN 978-0-8218-4286-7. ISSN 0271-4132.

2007

Johansson, Anders, Oberg, Anders and Pollicott, Mark (2007) Countable state shifts and uniqueness of g-measures. American Journal of Mathematics, Vol.129 (No.6). pp. 1501-1511. doi:10.1353/ajm.2007.0044 ISSN 0002-9327.

Jordan, T. and Pollicott, Mark (2007) Multifractal analysis and the variance of Gibbs measures. Journal of the London Mathematical Society, Vol.76 (No.1). pp. 57-72. doi:10.1112/jlms/jdm023 ISSN 0024-6107.

Pollicott, Mark and Sharp, Richard (2007) Pseudo-Anosov foliations on periodic surfaces. Topology and its Applications, Vol.154 (No.12). pp. 2365-2375. doi:10.1016/j.topol.2007.01.021 ISSN 0166-8641.

Jordan, Thomas, Pollicott, Mark and Simon, Karoly (2007) Hausdorff dimension for randomly perturbed self affine attractors. Communications in Mathematical Physics, Vol.270 (No.2). pp. 519-544. doi:10.1007/s00220-006-0161-7 ISSN 0010-3616.

Nair, R and Pollicott, Mark (2007) Pair correlations of sequences in higher dimensions. Israel Journal of Mathematics, Volume 157 (Number 1). pp. 219-238. doi:10.1007/s11856-006-0009-z ISSN 0021-2172.

Pollicott, Mark and Sharp, Richard (2007) Chebotarev-type theorems in homology classes. Proceedings of the American Mathematical Society, Vol.135 (No.12). pp. 3887-3894. doi:10.1090/S0002-9939-07-08923-X ISSN 0002-9939.

Pollicott, Mark (2007) Distribution of orbits for Mobius groups. In: Forni, G. and Lyubich, M. and Pugh, C. and Shub, M., (eds.) Partially Hyperbolic Dynamics, Laminations, and Teichmuller Flow. Fields Institute Communications, Volume 51 . American Mathematical Society, pp. 329-339. ISBN 9780821842744

2006

Csörnyei, M., Jordan, Thomas, Pollicott, Mark, Preiss, David and Solomyak, B. (2006) Positive-measure self-similar sets without interior. Ergodic Theory and Dynamical Systems, Vol.26 (No.3). pp. 755-758. doi:10.1017/S0143385705000702 ISSN 0143-3857.

Jordan, Thomas and Pollicott, Mark (2006) Properties of measures supported on fat Sierpinski carpets. Ergodic Theory and Dynamical Systems, Vol.26 (No.3). pp. 739-754. doi:10.1017/S0143385705000696 ISSN 0143-3857.