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:

Books

Rotation Sets and Complex Dynamics, Lecture Notes in Mathematics vol. 2214, Springer, 2018.

A Course in Complex Analysis, (13 chapters/441 pages/91 illustrations), 2018, to appear.

Papers

(With C. Petersen) On the Correspondence of External Rays Under Renormalization, 2019.

(With C. Petersen) On Combinatorial Types of Periodic Orbits of the Map $x \mapsto kx \ (\operatorname{mod} \ \mathbb Z)$. Part I: Realization, 2018, submitted for publication.

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.