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 -linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic -linear operators, for each . Indeed, the nonnormable spaces of entire functions and the countable product of lines support -linear operators with residual sets of hypercyclic vectors, for .
Juan Bès. J. Alberto Conejero. "An Extension of Hypercyclicity for -Linear Operators." Abstr. Appl. Anal. 2014 (SI20) 1 - 11, 2014. https://doi.org/10.1155/2014/609873