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

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

2003-08-04

arxiv.org/abs/math/0308020v1

Mathematics

Dynamical Systems

27 pages

Scientific paper

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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