Nonlinear Perron-Frobenius theorem for multi-homogeneous mappings

For matrices with nonnegative entries, the Perron-Frobenius theorem discusses existence, uniqueness, maximality and the computation of eigenvectors with nonnegative entries. This result has been generalized for homogeneous mappings leaving a cone invariant. More recently, Perron-Frobenius type results have been proved in multi-linear algebra, for the study of spectral problems involving tensors with nonnegative entries. We discuss a Perron Frobenius theorem for multi-homogeneous mappings which unify both of these generalizations in a single framework.