Mikko Stenlund

Ph.D., Postdoctoral Fellow

Email: firstname.lastname(at)helsinki.fi
Telephone:
Mobile: +1-917-365-0718

Mailing Address:
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York
NY 10012-1185
USA

Visiting Address:
Office 826

Scientific Activities:

I currently have a postdoctoral fellowship of the Academy of Finland until the fall of 2009. At Courant Institute I am involved, in addition to my other projects, in a line of research initiated by Lai-Sang Young. Broadly speaking, our aim is to study how to identify low dimensional phenomena in realistic dynamical systems of very high dimension by looking at suitable truncations of such a system. The work is motivated by physical applications, such as the flow of fluids. Moreover, I am making an effort to prove decay of correlations under compositions of maps that arise in Billiards / Lorentz gas related problems (see also my earlier work below).

After receiving my Ph.D. in June, 2006, I spent one year as a postdoc at Rutgers University, in the Mathematical Physics group run by Joel Lebowitz, with the support of the Finnish Cultural Foundation. During that time my interests began shifting heavily towards statistical methods in the study of dynamical systems. Together with my collaborators I studied the Random Toral Automorphism, which models the Lorentz gas with randomly positioned scatterers and is related to the motion of electrons in a metallic conductor. We were able to show that the system is exponentially mixing and to accurately relate the mixing rate to the "chaoticity" (Lyapunov exponent); see Publication 6. Furthermore, in Publication 7, we proved that the distribution of suitably normalized time averages of a smooth observable is asymptotically normal - even in a fixed environment.

My Ph.D. thesis (Publication 3) at the University of Helsinki dealt with the homoclinic splitting problem arising in a rapidly, quasiperiodically, forced pendulum. The advisor was Antti Kupiainen. Building on the thesis, I have recently written two articles. I construct the stable/unstable manifolds and study their detailed analyticity properties in Publication 4. Consequently, the splitting matrix has been studied in Publication 5, which in particular introduces a novel asymptotic expansion for the matrix and establishes an exponentially small upper bound on it with respect to the forcing rapidity.

I am also the author of two educational, expository, articles in international, peer-reviewed, journals. See publications 1 and 2.

My Master's Thesis was called "KAM Theorem and Renormalization" [PS].

Publications:

1. On the Tangent Lines of a Parabola. College Math. J. 32 (2001), no. 3, 194-196.
   
   
2. A Characterization of the Parabola. Math. Gaz. 89 (Nov 2005), no. 516, 507-511.
   
   
3. Homoclinic Splitting without Trees, Ph.D. thesis, University of Helsinki, May 2006. [http://urn.fi/URN:ISBN:952-10-3128-X]
4. Construction of Whiskers for the Quasiperiodically Forced Pendulum. Rev. Math. Phys. 19 (2007), no. 8, 823-877. [arXiv][mp_arc][Journal]
   
   
5. Asymptotic Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum. Submitted to Commun. Math. Phys. [arXiv][mp_arc]
   
   
6. Exponential Decay of Correlations for Randomly Chosen Hyperbolic Toral Automorphisms. Chaos 17 (2007), no. 4, 043116 (7 pages). (With Arvind Ayyer) [arXiv][mp_arc][Article]
   
   
7. Quenched CLT for Random Toral Automorphism. To appear in Discrete and Continuous Dynamical Systems A. (With Arvind Ayyer and Carlangelo Liverani) [arXiv][mp_arc]
   
   
8. Memory Loss for Time-Dependent Dynamical Dystems. To appear in Mathematical Research Letters. (With William Ott and Lai-Sang Young)

Recent and upcoming talks:

• Pendulum, Homoclinic Splitting, and Exponential Smallness. (Mathematical Physics Seminar, Rutgers University, 05.10.06)

• Asymptotic Expansion of the Homoclinic Splitting Matrix. (96th Statistical Mechanics Conference, 19.12.06)

• Current Problems in Nonequilibrium Statistical Mechanics. (Special Seminar at Helsinki University of Technology, 10.08.07)

• Quenched Central Limit Theorem for the Random Toral Automorphism. (Mathematical Physics Seminar, University of Helsinki, 15.08.07)

• Homoclinic Splitting in the Quasiperiodically Forced Pendulum. (Dynamics Seminar, Courant Institute, 13.11.07)

• Billiards and Statistical Properties of Toral Automorphisms. (Finnish Mathematical Days 2008, Helsinki University of Technology, 04.01.08)

• (Ergodic Theory and Statistical Mechanics Seminar, Princeton University, 14.02.08)

Honors:

• 2006 Rolf Nevanlinna doctoral thesis award

You might have met me here:

• ESI, June 2 - June 20