Invariant elliptic curves as attractors in the projective plane

TL;DR

This paper demonstrates that invariant elliptic curves with negative transverse Lyapunov exponents act as attractors in the projective plane, possessing dense orbits and positive measure basins.

Contribution

It establishes the attractor property of invariant elliptic curves with negative transverse Lyapunov exponents in rational maps on P^2.

Findings

Elliptic curves with negative transverse Lyapunov exponents are attractors.

Such curves have dense orbits.

Their basins have strictly positive measure.

Abstract

Let f be a rational self-map of P^2 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 is of strictly positive measure.