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POISSON PROCESSES FOR SUBSYSTEMS OF FINITE TYPE IN SYMBOLIC DYNAMICS

2009; World Scientific; Volume: 09; Issue: 03 Linguagem: Inglês

10.1142/s0219493709002713

1793-6799

Jean-René Chazottes, Zaqueu Coelho, Pierre Collet,

Quantum chaos and dynamical systems

Let Δ ⊊ V be a proper subset of the vertices V of the defining graph of an irreducible and aperiodic shift of finite type [Formula: see text]. Let Σ Δ be the subshift of allowable paths in the graph of [Formula: see text] which only passes through the vertices of Δ. For a random point x chosen with respect to an equilibrium state μ of a Hölder potential φ on [Formula: see text], let τ n be the point process defined as the sum of Dirac point masses at the times k > 0, suitably rescaled, for which the first n-symbols of T k x belong to Δ. We prove that this point process converges in law to a marked Poisson point process of constant parameter measure. The scale is related to the pressure of the restriction of φ to Σ Δ and the parameters of the limit law are explicitly computed.