Institutionen för Matematik - KTH

Undervisning

HT 24: SF2743 & SF1625

VT 25: SF2744 & SF1626

Useful links

Svenska matematikersamfundet

Chaos math

Research

My main research interests are in smooth dynamical systems. More specifically, I am interested in skew-product dynamical systems.

Editorial work

Mathematica Scandinavica (Associate editor)

Publications

• Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrödinger equations, Ergodic Theory Dynam. Systems 25 (2005), no. 4, 1015–1045.

• Positive Lyapunov exponents for continuous quasi-periodic Schrödinger equations, J. Math. Phys. 47 (2006), no. 2.

• Explicit examples of arbitrarily large analytic ergodic potentials with zero Lyapunov exponent, Geom. Funct. Anal. 16 (2006), no. 6, 1183--1200.

• Dynamics of the quasi-periodic Schrödinger cocycle at the lowest energy in the spectrum, Comm. Math. Phys. 272 (2007), 397--442.

• Positive Lyapunov exponent and minimality for the continuous 1-d quasi-periodic Schrödinger equation with two basic frequencies, Ann. Henri Poincaré 8 (2007), 687--730.

• Lyapunov exponents of continuous Schrodinger cocycles over irrational rotations (with D. Damanik and R. Johnson), Ann. Mat. Pura Appl. (4) 187 (2008), no. 1, 1--6.

• Minimal subsets of projective flows (with R. Johnson), Discrete Contin. Dyn. Syst. Ser. B 9 (2008), no. 3-4, 493--516.

• Universal asymptotics in hyperbolicity breakdown (with M. Saprykina), Nonlinearity 21 (2008), no. 3, 557--586.

• SNA's in the quasi-periodic quadratic family, Comm. Math. Phys. 286 (2009), 137--161.

• Rotation numbers for quasiperiodically forced circle maps --- mode locking vs strict monotonicity (with T. Jäger), J. Amer. Math. Soc. 22 (2009), 353--362.

• Quasi-periodic perturbation of unimodal maps exhibiting an attracting 3-cycle, Nonlinearity 25 (2012), no. 3, 683--741.

• Attractors in the quasi-periodically perturbed quadratic family. Nonlinearity 25 (2012), no. 5, 1537--1545.

• The dynamics of a class of quasi-periodic Schrödinger cocycles. Ann. Henri Poincaré 16 (2015), no. 4, 961–1031.

• A note on circle maps driven by strongly expanding endomorphisms on T. Dyn. Syst. 33 (2018), no. 2, 361–368.

• On some generalizations of skew-shifts on T². Ergodic Theory Dynam. Systems 39 (2019), no. 1, 19–61.

• Quasi-periodic kicking of circle diffeomorphisms having unique fixed points. Mosc. Math. J. 19 (2019), no. 2, 189–216.

• Positive fibered Lyapunov exponents for some quasi-periodically driven circle endomorphisms with critical points (with H. Eliasson). Astérisque No. 415.

• Some remarks on the dynamics of the almost Mathieu equation at critical coupling. Nonlinearity 33 (2020), no. 6, 2707–2722.

• Positive Lyapunov exponent for some Schrödinger cocycles over strongly expanding circle endomorphisms. Comm. Math. Phys. 379 (2020), no. 1, 353–360.

• Coexistence of ac and pp spectrum for kicked quasi-periodic potentials (with R. Krikorian). J. Spectr. Theory 11 (2021), no. 3, 1215–1254.

• On the Lyapunov exponents for a class of circle diffeomorphisms driven by expanding circle endomorphisms. J. Dynam. Differential Equations 34 (2022), no. 1, 107–114.

• Circle maps driven by a class of uniformly distributed sequences on T. Bull. Lond. Math. Soc. 54 (2022), no. 3, 910–928.

• Monotone families of circle diffeomorphisms driven by expanding circle maps (with R. Krikorian). Commun. Math. Phys. 405, 205 (2024).

My papers on MathSciNet

Thesis

My doctoral thesis "Dynamical Properties of Quasi-periodic Schrödinger Equations" can be found here.  And here I am in the Mathematics Genealogy Project.