Recent preprints

1. Amenable graphs and the spectral radius of extensions of Markov maps (with Manuel Stadlbauer and Elaine Rocha)  
   Preprint on Arxiv.
2. Bowen's formula for a rational graph-directed Markov system (with Tadashi Arimitsu, Hiroki Sumi and Takayuki Watanabe)  
   Preprint on Arxiv.
3. Large deviations of homological growth rates for hyperbolic surfaces (with Hiroki Takahasi)  
   Preprint on Arxiv.
4. Multifractal analysis of homological growth rates for hyperbolic surfaces (with Hiroki Takahasi)  
   Preprint on Arxiv.

Publications (peer-reviewed)

1. Thermodynamic formalism for transient dynamics on the real line (with Marc Kesseboehmer and Maik Groeger (Jagiellonian University))  
   Nonlinearity 35 (2022), 1093-1118.
2. Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches (with Hiroki Takahasi)  
   Adv. Math. 385 (2021).
3. A multifractal analysis for cuspidal windings on hyperbolic surfaces (with Marc Kesseboehmer and Sara Munday)  
   Stochastics and Dynamics, Online Ready, 2021
4. Multifractal Formalism for generalised local dimension spectra of Gibbs measures on the real line (with Hiroki Sumi)  
   Journal of Mathematical Analysis and Applications, Volume 491, Issue 2, 2020
5. Spectral gap property for random dynamics on the real line and multifractal analysis of generalised Takagi functions (with Hiroki Sumi)  
   Communications in Mathematical Physics volume 377, 2020
6. Normalizer, divergence type and Patterson measure for discrete groups of the Gromov hyperbolic space (with Katsuhiko Matsuzaki and Yasuhiro Yabuki)  
   Groups, Geometry, and Dynamics , Volume 14, Issue 2, 2020
7. Weighted cogrowth formula for free groups (with Katsuhiko Matsuzaki)  
   Groups, Geometry and Dynamics, Volume 14, Issue 2, 2020
8. 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.
9. Growth and cogrowth of normal subgroups of a free group (with Katsuhiko Matsuzaki)  
   Proc. Amer. Math Soc. 145 (2017), 4141-4149, Preprint on Arxiv.
10. Multifractal formalism for expanding rational semigroups and random complex dynamical systems (with Hiroki Sumi)  
    Nonlinearity 28 (2015) 2913-2938.
11. 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.
12. Group-extended Markov systems, amenability, and the Perron-Frobenius operator 
    Proc. Amer. Math. Soc. 143 (2015), 289-300.
13. Recurrence and pressure for group extensions 
    Ergodic Theory and Dynamical Systems 36 (2016), 108-126.
14. A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian Groups  
    J. Geom. Anal. 25 (2015), 289-305.
15. Conformal Fractals for Normal Subgroups of Free Groups 
    Conform. Geom. Dyn. 18 (2014), 31-55. Full-text PDF, free access.
16. 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.
17. Fractal Models for Normal Subgroups of Schottky Groups  
    Trans. Amer. Math. Soc. 366 (2014), 5453-5485.
18. 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.
19. 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
20. 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