
Kristian BjerklövProfessor i Matematik


HT 19: SF1625 (Period 1)
VT 20: SF2717 (period 4)
Dynamical systems and number theory at KTH
Svenska
matematikersamfundet
Chaos
math
My main research interests are in smooth dynamical systems. More specifically, I am interested in skewproduct dynamical systems.
Positive Lyapunov exponent and minimality for a class of onedimensional quasiperiodic Schrödinger equations, Ergodic Theory Dynam. Systems 25 (2005), no. 4, 1015–1045.
Positive Lyapunov exponents for continuous quasiperiodic 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, 11831200.
Dynamics of the quasiperiodic Schrödinger cocycle at the lowest energy in the spectrum, Comm. Math. Phys. 272 (2007), 397442.
Positive Lyapunov exponent and minimality for the continuous 1d quasiperiodic Schrödinger equation with two basic frequencies, Ann. Henri Poincaré 8 (2007), 687730.
Lyapunov exponents of continuous Schrodinger cocycles over irrational rotations (with D. Damanik and R. Johnson), Ann. Mat. Pura Appl. (4) 187 (2008), no. 1, 16.
Minimal subsets of projective flows (with R. Johnson), Discrete Contin. Dyn. Syst. Ser. B 9 (2008), no. 34, 493516.
Universal asymptotics in hyperbolicity breakdown (with M. Saprykina), Nonlinearity 21 (2008), no. 3, 557586.
SNA's in the quasiperiodic quadratic family, Comm. Math. Phys. 286 (2009), 137161.
Rotation numbers for quasiperiodically forced circle maps  mode locking vs strict monotonicity (with T. Jäger), J. Amer. Math. Soc. 22 (2009), 353362.
Quasiperiodic perturbation of unimodal maps exhibiting an attracting 3cycle, Nonlinearity 25 (2012), no. 3, 683741.
Attractors in the quasiperiodically perturbed quadratic family. Nonlinearity 25 (2012), no. 5, 15371545.
The dynamics of a class of quasiperiodic 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 skewshifts on T². Ergodic Theory Dynam. Systems 39 (2019), no. 1, 19–61.
Quasiperiodic kicking of circle diffeomorphisms having unique fixed points. Mosc. Math. J. 19 (2019), no. 2, 189–216.
Positive fibered Lyapunov exponents for some quasiperiodically driven circle endomorphisms with critical points (with H. Eliasson). To appear in Astérisque.
Some remarks on the dynamics of the almost Mathieu equation at critical coupling. To appear in Nonlinearity.
Coexistence of ac and pp spectrum for kicked quasiperiodic potentials (with R. Krikorian). To appear in J. Spectr. Theory.
Positive Lyapunov exponent for some Schrödinger cocycles over strongly expanding circle endomorphisms. To appear in Comm. Math. Phys.
On the Lyapunov exponents for a class of circle diffeomorphisms driven by expanding circle endomorphisms. To appear in J. Dynam. Differential Equations.
My papers on MathSciNet
My doctoral thesis "Dynamical Properties of Quasiperiodic
Schrödinger Equations" can be found here.
And here
I am in the Mathematics Genealogy Project.