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

J. Llibre, R. S. Mackay

Research output: Contribution to journalArticleResearchpeer-review

64 Citations (Scopus)

Abstract

We show that if a homeomorphism f 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 p/q, p ℤ2, q ℕ, in the interior of Δ, there is a periodic orbit of rotation vector p / q, and for every compact connected subset C of Δ there is an orbit whose rotation set is C. Finally, we prove that f has ‘toroidal chaos’. © 1991, Cambridge University Press. All rights reserved.
Original languageEnglish
Pages (from-to)115-128
JournalErgodic Theory and Dynamical Systems
Volume11
DOIs
Publication statusPublished - 1 Jan 1991

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