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 719

Scientific Activities:

I currently have a postdoctoral fellowship from the Academy of Finland. I am partially supported by Courant Institute where I am physically located and where I collaborate with Lai-Sang Young.

One of my aims is, broadly speaking, 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. I am also interested in hyperbolic dynamics. Most recently, I obtained the surprising result that for dispersing Billiards and transitive Anosov diffeomorphisms the Central Limit Theorem (i.e., asymptotic normality of observations) follows from a single pair correlation bound; Publication 11.

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:

On the Tangent Lines of a Parabola. College Math. J. 32 (2001), no. 3, 194-196.
A Characterization of the Parabola. Math. Gaz. 89 (Nov 2005), no. 516, 507-511.
Homoclinic Splitting without Trees, Ph.D. thesis, University of Helsinki, May 2006. [http://urn.fi/URN:ISBN:952-10-3128-X]
Construction of Whiskers for the Quasiperiodically Forced Pendulum. Rev. Math. Phys. 19 (2007), no. 8, 823-877. [arXiv][mp_arc][Article]
An Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum. Submitted. [arXiv][mp_arc]
Exponential Decay of Correlations for Randomly Chosen Hyperbolic Toral Automorphisms. Chaos 17 (2007), no. 4, 043116 (7 pp). (With Arvind Ayyer) [arXiv][mp_arc][Article]
Quenched CLT for Random Toral Automorphism. Discrete and Continuous Dynamical Systems A. 24 (2009), no. 2, 331-348. (With Arvind Ayyer and Carlangelo Liverani) [arXiv][mp_arc][Article]
Memory Loss for Time-Dependent Dynamical Systems. Math. Res. Lett. 16 (2009), no. 3, 463-475 (With William Ott and Lai-Sang Young) [Article]
Deterministic Walks in Quenched Random Environments of Chaotic Maps. J. Phys. A: Math. Theor. 42 (2009) 245101 (14 pp). (With Tapio Simula) [arXiv][Article]
From Limit Cycles to Strange Attractors. Submitted. (With William Ott) [mp_arc]
A Strong Pair Correlation Bound implies the CLT for Sinai Billiards. Submitted. [pdf][mp_arc]

In preparation:

Invariance Principles for a Random Toral Automorphism.

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. (96^th 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)
Memory Loss in Time-Dependent Dynamical Systems. (100^th Statistical Mechanics Conference, 16.12.08)
A Strong Pair-Correlation Bound implies the Central Limit Theorem for Sinai Billiards. (Special seminar, University of Helsinki, August 09)
(Dynamical Systems Seminar, Courant Institute, Sept 30, 09)
(Ergodic Theory and Statistical Mechanics Seminar, Princeton University, Oct 22, 09)
(Mathematical Physics Seminar, Rutgers University, Nov 5, 09)
(Dynamical Systems Seminar, Stony Brook University, Dec 4, 09)

Mikko Stenlund

Ph.D., Postdoctoral Fellow

Scientific Activities:

Publications:

In preparation:

Recent and upcoming talks:

Teaching:

Honors:

You might have met me here: