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Mathematics Institute

Publications of Mark Pollicott

"For twenty-five years he has been reading and writing things that clever men have long known and stupid ones are not interested in".
(Uncle Vanya on the Professor, by Chekov).

Books

As (co-)author

  1. Asterisque 187-8 (1990)  
  2. LMSLN 180 (1993)
  3. LMSST 40(1998)
  4. Asterisque 373 (2015)
  5. SLN 2206 (2017)

As (co-)editor

  1. LMSLN 228 (2006)
  2. PSPUM 89 (2015)
  3. SLN 2290

Papers published in 2013

  1. L. Magalhães and M. Pollicott, Geometry and dynamics of planar linkages. Comm. Math. Phys. 317 (2013) 615–634.
  2. M. Pollicott and R. Sharp, Ergodic theorems for actions of hyperbolic groups. Proc. Amer. Math. Soc. 141 (2013), no. 5, 1749–1757.
  3. M. Pollicott and R. Sharp, Correlations of length spectra for negatively curved manifolds. Comm. Math. Phys. 319 (2013) 515–533.
  4. P. Giulietti, C. Liverani, M. Pollicott, Anosov flows and dynamical zeta functions. Ann. of Math. (2) 178 (2013) 687–773

Papers published in 2014

  1. M. Pollicott and R. Sharp, Length asymptotics in higher Teichmüller theory. Proc. Amer. Math. Soc. 142 (2014) 101–112.
  2. M.Pollicott and P. Felton, Estimating Mahler measures using periodic points for the doubling map. Indag. Math. (N.S.) 25 (2014) 619–631.
  3. M. Pollicott and R. Sharp, A Weil-Petersson type metric on spaces of metric graphs. Geom. Dedicata 172 (2014), 229–244.
  4. O. Bandtlow, O. Jenkinson and M. Pollicott, Periodic points, escape rates and escape measures, in Ergodic theory, open dynamics, and coherent structures, 41–58, Springer Proc. Math. Stat., 70, Springer, New York, 2014.

Papers published in 2015

  1. F. Paulin, M. Pollicott and B. Schapira, Equilibrium states in negative curvature. Astérisque No. 373 (2015), viii+281 pp. ISBN: 978-2-85629-818-3
  2. D. Kagiso and M.Pollicott, Computing multifractal spectra. Dyn. Syst. 30 (2015) 404–425.
  3. J. Fraser and M. Pollicott, Micromeasure distributions and applications for conformally generated fractals. Math. Proc. Cambridge Philos. Soc. 159 (2015) 547–566.
  4. M. Pollicott, Analyticity of dimensions for hyperbolic surface diffeomorphisms. Proc. Amer. Math. Soc. 143 (2015), 3465–3474.
  5. M. Pollicott and P. Vytnova, Estimating singularity dimension. Math. Proc. Cambridge Philos. Soc. 158 (2015) 223–238.

Papers published in 2016

  1. M. Pollicott and R. Sharp, Weil-Petersson metrics, Manhattan curves and Hausdorff dimension. Math. Z. 282 (2016) 1007–1016.
  2. F. Paulin and M. Pollicott, Logarithm laws for equilibrium states in negative curvature. Comm. Math. Phys. 346 (2016), no. 1, 1–34.
  3. M. Pollicott and P. Vytnova, Linear response and periodic points. Nonlinearity 29 (2016) 3047–3066.

Papers published in 2017

  1. M. Pollicott, A Nonlinear Transfer Operator Theorem. J. Stat. Phys. 166 (2017), no. 3-4, 516–524.
  2. J. Fraser and M. Pollicott, Uniform scaling limits for ergodic measures. J. Fractal Geom. 4 (2017) 1–19.
  3. A. Johansson, A. Öberg and M. Pollicott, Ergodic theory of Kusuoka measures. J. Fractal Geom. 4 (2017) 185–214.
  4. S. Galatolo and M. Pollicott, Controlling the statistical properties of expanding maps. Nonlinearity 30 (2017) 2737–2751.
  5. M. Pollicott, A note on the shrinking sector problem for surfaces of variable negative curvature. (Russian) Tr. Mat. Inst. Steklova 297 (2017), Poryadok i Khaos v Dinamicheskikh Sistemakh, 281–291.
  6. M. Pollicott, Amenable covers for surfaces and growth of closed geodesics. Adv. Math. 319 (2017), 599–609.
  7. M. Pollicott and P. Vytnova, Critical points for the Hausdorff dimension of pairs of pants. Groups Geom. Dyn. 11 (2017), no. 4, 1497–1519.

Papers published in 2018

  1. O.Jenkinson, M. Pollicott, and P.Vytnova,Rigorous Computation of Diffusion Coefficients for Expanding Maps. J. Stat. Phys. 170 (2018), 221–253
  2. O.Jenkinson and M.Pollicott, Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: A hundred decimal digits for the dimension of E2. Adv. Math. 325 (2018), 87–115.
  3. Open Conformal Systems and Perturbations of Transfer Operators (with M.Urbanski), Lecture Notes in Mathematics 2206, Springer, Berlin, 2018 (ISBN 978-3-319-72178-1)
  4. Hyperbolic systems, zeta functions and other fields, Banach Center Publications, 115 (2018) 145-182
  5. Stationary measures associated to analytic iterated function schemes, (with I. Cipriano) Math. Nachr. 291 (2018), no. 7, 1049–1054
  6. Hyperbolic systems, zeta functions and other friends. Dynamical systems, 145–182, Banach Centre Publications, volume 115, Polish Acad. Sci. Inst. Math., Warsaw, 2018.
  7. Apollonius circle counting, London Math. Soc. Newsletter, No. 478 (2018) 31–34.
  8. Joint spectral radius, Sturmian measures and the finiteness conjecture (with O. Jenkinson), Ergodic Theory and Dynamical Systems, 38 (2018) 3062-3100.

Papers published in 2019

  1. Phase transitions in long-range Ising models and an optimal condition for factors of g-measures (with A. Johansson and A. Oberg), Ergodic Theory and Dynamical Systems, 39 (2019) 1317-1330

  2. Zeros of the Selberg zeta function for non-compact surfaces (with P. Vytnova), Geomtriae Dedicata, 201 (2019), 155–186

Papers published in 2020

  1. Volume growth for infinite graphs and translation surfaces (with P. Colognese), Contemporary Mathematics, 744, (2020) 109–123

  2. Rigorous dimension estimates for Cantor sets arising in Zaremba theory, (with O. Jenkinson), Contemporary Mathematics, 744, (2020) 83-107

Papers published in 2021

  1. Dynamical zeta functions and the distribution of orbits. Handbook of group actions. V, 399–440,
  2. The Schottky-Klein prime function and counting functions for Fenchel double crosses. Monatsh. Math. 195 (2021), no. 2, 323–342
  3. Fourier multipliers and transfer operators. J. Fractal Geom. 8 (2021), no. 2, 189–199.
  4. Asymptotic counting in conformal dynamical systems, (with M. Urbanski) Mem. Amer. Math. Soc. 271 (2021), no. 1327, v+139 pp. ISBN: 978-1-4704-6577-3
  5. How many inflections are there in the Lyapunov spectrum? (with O. Jenkinson and P. Vytnova), Comm. Math. Phys. 386 (2021), no. 3, 1383–1411.
  6. Effective estimates of Lyapunov exponents for random products of positive matrices. Nonlinearity 34 (2021), no. 10, 6705–6718.
  7. Statistical properties of the Rauzy-Veech-Zorich map (with R.Aimino), in Thermodynamic formalism, Springer Lecture Notes in Mathematics vol. 2290, 317-349.
  8. Higher Teichmüller theory for surface groups and shifts of finite type (with R. Sharp), in Thermodynamic formalism, Springer Lecture Notes in Mathematics vol. 2290, 395-418.

Papers published in 2022

  1. Uniform lower bounds on the dimension of Bernoulli convolutions.(with V. Klepsyn and P. Vytnova), Advances in Mathematics, 395 (2022) Paper No. 108090, 55 pp.
  2. Gibbs measures for hyperbolic attractors defined by densities (with D. Parmenter), Discrete Contin. Dyn. Syst. 42 (2022), no. 8, 3953–
  3. Minimizing entropy for translation surfaces (with P. Colognese) Conform. Geom. Dyn.26 (2022) 97-110
  4. Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra, (with C.Matheus, C.Moreira and P. Vytnova),Adv.Math 409 (2022)
  5. Comparison theorems for closed geodesics on negatively curved surfaces (with S.Cantrell), Groups Geom Dyn 16 (2022) 461-491
  6. Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups (with P. Vytnova) Trans. Amer. Math. Soc. 9 (2022) 1102-1159

Papers published in 2023

  1. Explicit examples of resonances for Anosov maps of the torus (with B.Sewell) Nonlinearity 36 (2023) 110-132
  2. Accurate bounds on Lyapunov exponents for expanding maps of the interval (with P. Vytnova) Comm. Math. Phys. 397 (2023), no. 1, 485–502
  3.  Groups, Drift and Harmonic Measures (with P. Vytnova), LNM 2312, Springer, Cham, 2023, 301–311
  4. An upper bound on the dimension of the Rauzy gasket, Bull. Soc.Math.France, 151 (2023) 595-611 (with B. Sewell)

Papers published in 2024

  1. Zeta functions in Teichmuller Theory, Math. Z. 306 (2024) 20pp (with R. Sharp)
  2. A dynamical approach to validated dynamics, (with ). Jenkinson) pp. 168-206 in A Vision for Dynamics in the 21st Century
    The Legacy of Anatole Katok, CUP, Cambridge 2024