Diffeomorphisms with infinitely many irrational invariant curves

Abstract

AbstractFor a surface diffeomorphism f∈Diff l(M), with l≥8, we prove that if f exhibits a non-transversal heteroclinic cycle composed of two fixed saddle points Q1 and Q2, one dissipative and the other expansive, then there exists an open set 𝒱⊂Diff l(M) such that $ f \in \overline {\mathcal {V}}$ and there exists a dense set 𝒟⊂𝒱 such that for all g∈𝒟, g exhibits infinitely many invariant periodic curves with irrational rotation numbers. Moreover, these curves are C1 conjugated to an irrational rotation on 𝕊1.