Rotation vectors and entropy for homeomorphisms of the torus isotopic to the identity

DOI Web Site 1 Citations

Description

<jats:title>Abstract</jats:title><jats:p>We show that if a homeomorphism <jats:italic>f</jats:italic> of the torus, isotopic to the identity, has three or more periodic orbits with non-collinear rotation vectors, then it has positive topological entropy. Furthermore, for each point ρ of the convex hull Δ of their rotation vectors, there is an orbit of rotation vector ρ, for each rational point <jats:italic>p</jats:italic>/<jats:italic>q</jats:italic>, <jats:italic>p</jats:italic> ∈ ℤ<jats:sup>2</jats:sup>, <jats:italic>q</jats:italic> ∈ ℕ, in the interior of Δ, there is a periodic orbit of rotation vector <jats:italic>p</jats:italic> / <jats:italic>q</jats:italic>, and for every compact connected subset <jats:italic>C</jats:italic> of Δ there is an orbit whose rotation set is <jats:italic>C</jats:italic>. Finally, we prove that <jats:italic>f</jats:italic> has ‘toroidal chaos’.</jats:p>

Journal

Citations (1)*help

See more

Details 詳細情報について

Report a problem

Back to top