EIGENVALUES of FIBONACCI STOCHASTIC ADDING MACHINE

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processo FAPESP: 03/03107-9

Processo FAPESP: 08/02841-4

In this work, we compute the eigenvalues of the transition operator associated to the Fibonacci stochastic adding machine. In particular, we show that the eigenvalues are connected to the set kappa of complex numbers z where (z(2), z) belongs to the filled Julia set of a particular endomorphism of C(2). We also study some topological properties of the set kappa.