Invariant Elliptic Curves as Attractors in the Projective Plane

Johan Taflin (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

Let f be a rational self-map of ℙ2 which leaves invariant an elliptic curve C with strictly negative transverse Lyapunov exponent. We show that C is an attractor, i.e. it possesses a dense orbit and its basin has strictly positive measure.

Mots clés: Attractor; Lyapunov exponent

Domaines: Mathématiques [math]

Johan Taflin. Invariant Elliptic Curves as Attractors in the Projective Plane. Journal of Geometric Analysis, 2010, 20 (1), pp.219-225. ⟨hal-01974293⟩