My main area of reseach is dynamical systems, especially holomorphic dynamics. I also have strong interests in complex analysis, Teichmuller theory and quasiconformal mappings, hyperbolic geometry and Kleinian groups, and geometric theory of foliations and laminations.

The following is a list of my publications in reverse
chronological order:

(With C. Petersen) On Combinatorial Types of Periodic Orbits of the Map $x \mapsto kx \ (\operatorname{mod} \ \mathbb Z)$. Part I: Realization, 2017, submitted for publication.

Rotation Sets and Complex Dynamics, research monograph, to appear as vol. 2214 in Springer series *Lecture Notes in Mathematics*.

Conformal Fitness and Uniformization of Holomorphically Moving Disks, Trans. Amer. Math. Soc. **368** (2016) 1023-1049.

(With V. Erlandsson) On Margulis Cusps of Hyperbolic 4-Manifolds,
Geometriae Dedicata **174** (2015) 75-103.

(With V. Erlandsson) A Discreteness Criterion for Groups Containing Screw Translations, Contemp Math. **639** (2015) 235-242.

On Siegel Disks of a Class of Entire
Maps, Duke Math. Journal **152** (2010) 481-532.

On
Boundary Homeomorphisms of Trans-quasiconformal Maps of the Disk
, Ann. Acad. Sci. Fenn. **33** (2008) 241-260.

On Biaccessible Points of the Mandelbrot Set, Proc. Amer. Math. Soc. **134** (2006) 2239-2250.

David Maps and Hausdorff Dimension, Ann. Acad. Sci. Fenn. **29** (2004) 121-138.

(With C. Petersen) On the Julia Set of a Typical Quadratic Polynomial with a Siegel Disk, Annals of Math **159** (2004) 1-52.

External Rays and the Real Slice of the Mandelbrot Set, Ergod. Th. & Dyn. Sys. **23** (2003) 637-660.

Old and New on Quadratic Siegel Disks , In *Shahyad*, a volume dedicated to Siavash Shahshahani on the occasion of his 60th birthday, 2002.

Shahshahani's Work in Dynamical Systems, In *Shahyad*, a volume dedicated to Siavash Shahshahani on the occasion of his 60th birthday, 2002.

Dynamics of Singular Holomorphic Foliations on the Complex Projective Plane, in ``Laminations and Foliations in Geometry, Topology, and Dynamics,'' M. Lyubich, J. Milnor, Y. Minsky (eds.), Contemporary Math. **269**, Amer. Math. Soc., 2001.

(With M. Yampolsky) Mating Siegel Quadratic Polynomials, J. Amer. Math. Soc. **14** (2001) 25-78.

Biaccessibility in Quadratic Julia Sets, Ergod. Th. & Dyn. Sys. **20** (2000) 1859-1883.

(With D. Schleicher) On Biaccessible Points in the Julia Set of a Cremer Quadratic Polynomial, Proc. Amer. Math. Soc. **128** (2000) 933-937.

Dynamics of Cubic Siegel Polynomials, Commun. Math. Phys. **206** (1999) 185-233.

On Critical Points of Proper Holomorphic Maps on the Unit Disk, Bull. London Math. Soc. **30** (1998) 62-66.

(With M. Zeinalian) When Ellipses Look Like Circles: The Measurable Riemann Mapping Theorem, Nashr-e-Riazi, **8** (1996) 5-14.

On Arithmetical Difference of Two Cantor Sets, IPM Technical Report, 1992/1.

(With C. Lucas) A generalized prey-predator model: Asymptotic behavior and catastrophes, Proceedings of the Conference in Applied Mathematics, Amir-Kabir University, Tehran, 1989.