Critical Intermittency in Random Interval Maps

Ale Jan Homburg; Charlene Kalle; Marks Ruziboev; Evgeny Verbitskiy; Benthen Zeegers

doi:10.1007/s00220-022-04396-9

Critical Intermittency in Random Interval Maps

Ale Jan Homburg, Charlene Kalle, Marks Ruziboev, Evgeny Verbitskiy, Benthen Zeegers^*

^*Corresponding author for this work

Dynamical Systems, Geometry and Mathematical Physics

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

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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 for any 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.

Original language	English
Pages (from-to)	1-37
Number of pages	37
Journal	Communications in Mathematical Physics
Volume	394
Issue number	1
DOIs	https://doi.org/10.1007/s00220-022-04396-9
Publication status	Published - Aug-2022

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title = "Critical Intermittency in Random Interval Maps",

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 Lq for any 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.",

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AU - Homburg, Ale Jan

AU - Kalle, Charlene

AU - Ruziboev, Marks

AU - Verbitskiy, Evgeny

AU - Zeegers, Benthen

N1 - Funding Information: We would like to thank Sebastian van Strien for valuable discussions and useful suggestions. The third author was partially funded by Lise Meitner Fellowship FWF M-2816. Publisher Copyright: © 2022, The Author(s).

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N2 - 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 Lq for any 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.

AB - 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 Lq for any 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.

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Critical Intermittency in Random Interval Maps

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