Packing Subordinacy With Application to Spectral Continuity

Abstract

By using methods of subordinacy theory, we study packing continuity properties of spectral measures of discrete one-dimensional Schrödinger operators acting on the whole line. Then we apply these methods to Sturmian operators with rotation numbers of quasibounded density to show that they have purely $\unicode[STIX]{x1D6FC}$-packing continuous spectrum. A dimensional stability result is also mentioned.

Forward boundedness of the trace map for the period doubling substitution

“…The result has further applications to packing continuity properties [1,2,6,7], which are subject of current research. Bounding forward orbits by a constant is an improvement on the weak bound for the trace map in [4] (lemma 5), which is the only known bound since the interest on the period doubling sequence in the context of Schrödinger operators began.…”