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

Manuela Giampieri; Stefano Isola

doi:10.3934/dcds.2005.12.115

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2005, Volume 12, Issue 1: 115-136. Doi: 10.3934/dcds.2005.12.115

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

Manuela Giampieri^1, and
Stefano Isola^2,

1.
Dipartimento di Matematica, Università di Roma 'Tor Vergata', Via della Ricerca Scientifica, I-00133 Roma
2.
Dipartimento di Matematica e Informatica, Università di Camerino, via Madonna delle Carceri, I-62032 Camerino

Received: June 30, 2003

Revised: August 31, 2004

Published: March 2005

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Abstract

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.

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

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