Recent preprints

  1. Multifractal Formalism for generalised local dimension spectra of Gibbs measures on the real line (with Hiroki Sumi)  
    Preprint on Arxiv.
  2. Spectral gap property for random dynamics on the real line and multifractal analysis of generalised Takagi functions (with Hiroki Sumi)  
    Preprint on Arxiv.
  3. Thermodynamic formalism for transient dynamics on the real line (with Marc Kesseboehmer and Maik Groeger (Univ. Vienna))  
    Preprint on Arxiv.
  4. A multifractal analysis for cuspidal windings on hyperbolic surfaces (with Marc Kesseboehmer and Sara Munday)  
    Preprint on Arxiv.
  5. Normalizer, divergence type and Patterson measure for discrete groups of the Gromov hyperbolic space (with Katsuhiko Matsuzaki and Yasuhiro Yabuki)  
    Preprint on Arxiv.

Publications (peer-reviewed)

  1. Weighted cogrowth formula for free groups (with Katsuhiko Matsuzaki)  
    Groups, Geometry and Dynamics, to appear, Preprint on Arxiv.
  2. Pointwise Hoelder exponents of the complex analogues of the Takagi function in random complex dynamics (with Hiroki Sumi)
    Adv. Math. 313 (2017) 839-874, Arxiv.
  3. Growth and cogrowth of normal subgroups of a free group (with Katsuhiko Matsuzaki)  
    Proc. Amer. Math Soc. 145 (2017), 4141-4149, Preprint on Arxiv.
  4. Multifractal formalism for expanding rational semigroups and random complex dynamical systems (with Hiroki Sumi)  
    Nonlinearity 28 (2015) 2913-2938.
  5. Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method (with Hiroki Sumi)  
    Trans. Amer. Math. Soc. 369 (2017), no. 9, 6147-6187, Preprint on arXiv.
  6. Group-extended Markov systems, amenability, and the Perron-Frobenius operator 
    Proc. Amer. Math. Soc. 143 (2015), 289-300.
  7. Recurrence and pressure for group extensions 
    Ergodic Theory and Dynamical Systems 36 (2016), 108-126.
  8. A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups  
    J. Geom. Anal. 25 (2015), 289-305.
  9. Conformal Fractals for Normal Subgroups of Free Groups 
    Conform. Geom. Dyn. 18 (2014), 31-55. Full-text PDF, free access.
  10. A Frechet law and an Erdoes-Philipp law for maximal cuspidal windings   (with Marc Kesseboehmer and Bernd Stratmann)
    Ergodic Theory and Dynamical Systems 22, (2013), 1008-2028.
  11. Fractal Models for Normal Subgroups of Schottky Groups  
    Trans. Amer. Math. Soc. 366 (2014), 5453-5485.
  12. Induced topological pressure for countable state Markov shifts (with Marc Kesseboehmer and Sanaz Lamei) 
    Stochastics and Dynamics 14, No. 2 (2014) doi:10.1142/S0219493713500160.
  13. Regularity of multifractal spectra of conformal iterated function systems (with Marc Kesseboehmer
    Trans. Amer. Math. Soc. 363 (2011), no. 1, 313-330. doi:10.1090/S0002-9947-2010-05326-7
  14. The arithmetic-geometric scaling spectrum for continued fractions (with Marc Kesseboehmer(pdf)
    Arkiv foer Matematik 48 (2010), no. 2 doi:10.1007/s11512-009-0102-8

Conference proceedings, research reports, other writings

  1. Hoelder regularity of limit state functions in random complex dynamical systems (with Hiroki Sumi)  
    RIMS Kokyuroku, 2015 (4).
  2. Hoelder regularity of the complex analogues of the Cantor function and the Takagi function (with Hiroki Sumi)  
    in Report No. 46/2014 of the Mathematisches Forschungsinstitut Oberwolfach, 2014.


  1. Thermodynamic Formalism for Group-Extended Markov Systems with Applications to Fuchsian Groups  
    Doctorate thesis, University Bremen, 2011,
  2. Exhausting Principles for the Thermodynamic Formalism of Countable State Markov Shifts with Applications to Continued Fractions
    Diploma thesis 2008