January  2005, 12(1): 115-136. doi: 10.3934/dcds.2005.12.115

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

1. 

Dipartimento di Matematica, Università di Roma 'Tor Vergata', Via della Ricerca Scientifica, I-00133 Roma, Italy

2. 

Dipartimento di Matematica e Informatica, Università di Camerino, via Madonna delle Carceri, I-62032 Camerino, Italy

Received  July 2003 Revised  September 2004 Published  December 2004

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.
Citation: Manuela Giampieri, Stefano Isola. A one-parameter family of analytic Markov maps with an intermittency transition. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 115-136. doi: 10.3934/dcds.2005.12.115
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