Institutionen för Matematik - KTH

Undervisning

SF2720, Kaotiska dynamiska system

SF1624, Algebra och geometri för COPEN (inloggning I KTH-Social)

SF1659, Matematik, baskurs, för CDATE (inloggning I KTH-Social)

Tidigare undervisning

SF1625, Envariabelanalys för CINEK, ht 2011 (inloggning i KTH-Social)

SF1625, Envariabelanalys för CSAMH, ht 2011 (inloggning i KTH-Social)

SF1625, Envariabelanalys för I, ht 2010

SF2720, Kaotiska dynamiska system, ht 2010

SF1625, Envariabelanalys, ht 2009
SF1637, Diff och trans III, ht 2009

SF1643, Tal och funktioner, ht 2008
SF1637, Diff och trans III, ht 2008

Useful links

Dynamical systems and number theory at KTH

Seminar in analysis and dynamical systems

Dynamical trends in Analysis, KTH, May 27-- 30,  2009.

Research

My main research interests are in smooth dynamical systems.

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.

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.