Modulus of Continuity for Peierls’s Barrier

Abstract

For an exact area preserving monotone twist diffeomorphism with a uniform lower bound β for the amount of twisting, we will show that Peierls’s barrier satisfies

$$ \left| {{P_{p/q}}\left( \xi \right) - {P_\omega }\left( \xi \right)} \right| \leqslant C\left( {{q^{ - 1}} + \left| {\omega q - p} \right|} \right) $$

, where C = (1200)cotβ.

Partially supported by National Science Foundation Grant No. DMS85-04984.