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# A one-parameter family of analytic Markov maps with an intermittency transition

• In 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.
Mathematics Subject Classification: 58F20, 58F25, 11F72, 11M26.

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