Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we show that the rotation distance between two ordered trees is fixed-parameter tractable, in the parameter, k, the rotation distance. The proof relies on the kern...

The problem of controlling the position of a pair of point vortices using a strain field or a field of a single souce/sink is considered. The problem dimension is reduced by averaging over the fast rotation of vortices around the center of vorticity. Control is assumed to be function of rotation phase only. For the case of the strain field actuation, optimal control problem is posed in three di...

– We prove that in finite time a trajectory of a Lipschitz vector field in R can not have infinite rotation around a given point. This result extends to the mutual rotation of two trajectories of a field in R: this rotation is bounded from above on any finite time interval. The bounds we give are only in terms of the Lipschitz constant of the field and the length of the time interval.

We examine the rotational dynamics associated with bounded chaotic flows, such as those on chaotic attractors, and find that the dynamics typically exhibits on-off intermittency. In particular, a properly defined chaotic rotation tends to follow, approximately, the phase-space rotation of a harmonic oscillator with occasional bursts away from this nearly uniform rotation. The intermittent behav...

In this paper we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schrödinger operators with Sturmian potentials. We apply this method to the transfer matrices in order to study the Lyapunov exponent and the growth rate of eigenfunctions. This gives uniform vanishing of the Lyapunov exponent on the spectrum for all irrational rotation numbers. For i...