An Extension of Hypercyclicity for N -Linear Operators

Abstract EN

Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators.

We propose an alternative notion of orbit for N -linear operators that is inspired by difference equations.

Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N -linear operators, for each N ≥ 2 .

Indeed, the nonnormable spaces of entire functions and the countable product of lines support N -linear operators with residual sets of hypercyclic vectors, for N = 2 .