Critical Intermittency in Random Interval Maps
Communications in Mathematical Physics, vol. 394, pp. 1–37
Abstract
Abstract Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function systems of interval maps and demonstrate the existence of a phase transition when varying probabilities, where the absolutely continuous stationary measure changes between finite and infinite. We discuss further properties of this stationary measure and show that its density is not in $$L^q$$ L q for any $$q>1$$ q > 1 . This provides a theory of critical intermittency alongside the theory for the well studied Manneville–Pomeau maps, where the intermittency is caused by a neutral fixed point.
Authors 5
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Vrije Universiteit Amsterdam · University of Amsterdam
Affiliation as printed
Department of Mathematics, VU University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands
KdV Institute for Mathematics, University of Amsterdam, Science Park 107, 1098 XG, Amsterdam, The Netherlands
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Affiliation as printed
Mathematical Institute, University of Leiden, PO Box 9512, 2300 RA, Leiden, The Netherlands
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Leiden University · University of Vienna
Affiliation as printed
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Vienna, Austria
Mathematical Institute, University of Leiden, PO Box 9512, 2300 RA, Leiden, The Netherlands
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Leiden University · University of Groningen
Affiliation as printed
Bernoulli Institute, University of Groningen, Nijenborgh 9, 9747 AG, Groningen, The Netherlands
Mathematical Institute, University of Leiden, PO Box 9512, 2300 RA, Leiden, The Netherlands
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Affiliation as printed
Mathematical Institute, University of Leiden, PO Box 9512, 2300 RA, Leiden, The Netherlands
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