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Chaotic polynomials on Fréchet spaces
Authors:Alfredo Peris
Institution:Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
Abstract:Contrary to the case of polynomials on Banach spaces, in which it is known that no hypercyclic homogeneous polynomial of degree $m \geq 2$ exists on any Banach space, we construct for each $m \geq 2$ a chaotic $m$-homogeneous polynomial $P$ on the Fréchet space ${\cal H}(\mathbb C)$.

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