Original scientific paper

Accelerating orbits of twist diffeomorphism on a torus

Siniša Slijepčević

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.

Keywords

Area-preserving; twist diffeomorphism; connecting orbits; Frenkel-Kontorova model; topological entropy; metric entropy

Hrčak ID:

6402

URI

https://hrcak.srce.hr/6402

Publication date:

1.6.1999.

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