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

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

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

Pollicott, Mark (2018) Appolonius circle counting. LMS Newsletter, 478 .

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

Pollicott, Mark (2018) Hyperbolic systems, zeta functions and other friends. Proceedings of the Banach Centre, 115 . (In Press)

Pollicott, Mark and Urbanski, Mariuski (2018) Asymptotic counting in conformal dynamical systems. Memoirs of the American Mathematical Society . (In Press)

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

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

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

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

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.

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.

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

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).

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

2015

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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

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

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. ISSN 0271-4132. doi:10.1090/conm/484

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. ISSN 0016-2736. doi:10.4064/fm206-0-15

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. ISSN 0016-2736. doi:10.4064/fm206-0-10

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

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

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

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

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

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.

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

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

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

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

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

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

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

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