Christian Henriksen

I'm interested in dynamical systems, and in particular holomorphic dynamics in one variable, as well as industrial mathematics. I am associate lector at Technical University of Denmark.

Department of Mathematics
Technical University of Denmark
Matematiktorvet, building 303
2800 Kgs. Lynbgy
DENMARK

phone (45) 4525 3054
fax (45) 4588 1399
E-mail christian.henriksen@mat.dtu.dk

Teaching

This semester I am teaching

• 01005 Mathematics 1,
• 02490 Pilot study of your own project idea, and a
• Special course in complex analysis.

Projects

I'm currently thinking about four different projects: Universality, Teichmüller space of an entire function, Weierstrass method and Arnold disks.

Universality in holomorphic dynamics

The aim is to generalize universality results of McMullen to higher dimensional paramter spaces.

Teichmüller space of an entire function

With Núria Fagella: Rational mappings does not admit wandering domains. This was demonstrated by Sullivan by showing that this would imply that the Teichmüller space of the map then would be infinite. Entire mappings can have infinite Teichmüller spaces and allow for other phenomena that is impossible for rational maps such as Baker domain. Does an entire function with a Baker Domain have an infinitely dimensional Teichmüller space? Not necessarily...

Weierstrass Method

With Xavier Buff: Weierstrass method is an iterative method that allows you to simultaneously locate all the zeroes of a polynomial.

Arnold disks

Click on the animation to the right to see more animations with a short description.

With X. Buff, N. Fagella and L. Geyer: We consider a certain two-parameter family of rational maps, and are interested in knowing the geometry of the set of parameters for which the corresponding maps possesses a fixed Herman Ring of a given rotation number. For sufficiently irrational rotation numbers this is a (holomorphically embedded) disk.

Short CV

• 2006 Employed at Technical University of Denmark as associate professor.
• 2003-2006 Employed at Technical University of Denmark via a Steno stipend.
  
• 2001-2002 employed at Université Paul Sabatier via a Marie Curie fellowship;
• 2000 (second half) employed as ammanuensis at Technical University of Denmark;
• 2000 obtained ph.d. degree at Technical University of Denmark;
• 1997 obtained master degree at Technical University of Denmark.
  

Publications

Theses

• Holomorphic Dynamics and Herman Rings. Master thesis, 100 pages, (1997).
• Topics in Holomorphic Dynamics. Ph.D.-thesis, 113 pages. (2000).

Publications in peer-reviewed journals

• With X. Buff; Scaling ratios and triangles in Siegel disks. Math. Res. Lett. 6 (1999), no. 3-4, 293--305.
• With J. Gravesen; The geometry of the scroll compressor. SIAM Rev. 43 (2001), no. 1, 113--126 (electronic).
• With X. Buff, J. H. Hubbard; Farey curves. Experiment. Math. 10 (2001), no. 4, 481--486.
• Blaschke products and proper holomorphic mappings. J. Geom. Anal. 11 (2001), no. 4, 619--625.
• With X. Buff; Julia sets in parameter spaces. Comm. Math. Phys. 220 (2001), no. 2, 333--375.
• With X. Buff; On König's root finding algorithms. Nonlinearity 16 (2003), no. 3, 989--1015.
• The Combinatorial Rigidity Conjecture is False for Cubic Polynomials. Trans. Amer. Math. Soc. 355 (2003), no. 9, 3625--3639 .
• With N. Fagella; Deformation of Entire Mappings with Baker Domains. Discrete Contin. Dyn. Syst. 15 (2006), No. 2, 379--394.
• With X. Buff, N. Fagella and L. Geyer; Arnold Disks and Herman Rings. J. London Math. Soc. (2) 72 (2005), no. 3, 689--716.

Proceedings

• With G. Ble, A. Douady; Round Annuli. Contemporary Mathematics Volume 355, 2004: "In the Tradition of Ahlfors and Bers, III."
• With N. Fagella; Arnold Disks and the Moduli of Herman Rings of the Complex Standard Family. Hjorth, Paul G. (ed.) et al., Dynamics on the Riemann sphere. A Bodil Branner Festschrift. Zürich: European Mathematical Society Publishing House (ISBN 3-03719-011-6/hbk). 161--182 (2006).
• With N. Fagella; The Teichmüller space of an entire function. Schleicher, Dierk (ed.), Complex dynamics. Families and friends. Wellesley, MA: A K Peters (ISBN 978-1-56881-450-6/hbk). 297-330 (2009).