Abstract. Given an area-preserving twist diffeomorphism on 2D torus, we prove existence of orbits asymptotic to arbitrary periodic or quasiperiodic Aubry-Mather minimising set and with arbitrary shear rotation number from the shear rotation interval; and orbits whose ends have two arbitrary shear rotation numbers from the shear rotation interval. As a corollary, we construct infinitely many ergodic measures with positive metric entropy supported on the set of accelerating orbits, and therefore mutually singular with the invariant measure contructed by J.N. Mather and G. Forni.
1991 Mathematics Subject Classification. 58F13, 58F08.
Key words and phrases. Area-preserving, twist diffeomorphism, connecting orbits, Frenkel-Kontorova model, topological entropy, metric entropy.