Ergodic properties of a semilinear partial differential equation.

Semiflows on some spaces of continuous functions generated by a semilinear partial differential equation are studied. Sufficient conditions for the existence of invariant measures with strong ergodic properties are given. These properties imply chaotic behaviour of the semiflows, that is, the existence of dense trajectories and that each trajectory is unstable. In the proofs we use the Lévy d -parameter Brownian motion and we show that these semiflows are isomorphic with translation along the radii. [ABSTRACT FROM AUTHOR]