Area-preserving irrotational diffeomorphisms of the torus with sublinear diffusion

Abstract

We construct a $C^{\infty }$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose rotation set is $\{(0,0)\}$, which in addition has the property that almost every orbit by the lifted dynamics is unbounded and accumulates in every direction of the circle at infinity.

8 pages

References in corpus (1)

• Dynamics of homeomorphisms of the torus homotopic to Dehn twists

Cited by in corpus (9)

• Uniform bounds for diffeomorphisms of the torus and a conjecture of P. Boyland
• On annular maps of the torus and sublinear diffusion
• On the dynamics of minimal homeomorphisms of ${\mathbb{T}}^2$ which are not pseudo-rotations
• Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms
• Ergodicity and annular homeomorphisms of the torus
• On torus homeomorphisms whose rotation set is an interval
• On non-contractible periodic orbits for surface homeomorphisms
• A characterization of annularity for area-preserving toral homeomorphisms
• Inexistence of sublinear diffusion for a class of torus homeomorphisms