2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68232In this paper we introduce and study a one-parameter family of piecewise analytic interval maps having the tent map and the Farey map as extrema. Among other things, we construct a Hilbert space of analytic functions left invariant by the Perron-Frobenius operator of all these maps and study the transition between discrete and continuous spectrum when approaching the intermittent situation.27 pagesDynamical SystemsSpectral TheoryAMS Subject Classification: 58F20, 58F25, 11F72, 11M26text