Extended States for the Schrodinger Operator with

Quasi-Periodic Potential in Dimension Two

The operator [H.sub.0] describes a well-understood system with [V.sub.n] being the background periodic or

quasi-periodic potential.

Qi, "Bilinear approach to

quasi-periodic wave solutions of the Kersten-Krasil'shchik coupled KdV-mKdV system," Boundary Value Problems, p.

The domains grew through the crystal and appeared at the opposite polar surface as

quasi-periodic chains of isolated hexagonal microdomains (Figure 1(f)), which merged to the "dashed" structure (Figure 1(g)) for middle D values.

The question about the reducibility of

quasi-periodic systems plays an important role in the theory of ordinary differential equations.

On Saturn, it's known as

Quasi-Periodic Oscillation (QPO) and Quasi-Quadrennial Oscillation (QQO) on Jupiter.

So, the heart sounds are

quasi-periodic. The degree of the periodic property can be reflected by the sharpness of the peak.

Finally, after 20-25 laser scans, a granular film is formed with an average height of the relief of 52nm (Figure 5(a)), which differs from the

quasi-periodic nanoparticle arrays obtained for smaller number of laser passages at smaller laser speed (Figure 5(b)).

Qin, "A kind of explicit

quasi-periodic solution and its limit for the Toda lattice equation," Modern Physics Letters B, vol.

We will focus in particular on predictability in the vicinity of bifurcations leading to intermittent and

quasi-periodic dynamics.

Although only four scattered and isolated points are observed in the Poincare maps shown in Figures 10(d), 11(d), 16(d), and 17(d), the enlarged graphic circulated by the red circle shows that the isolated "points" are actually closed loops which indicate

quasi-periodic motion.