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Critical states of transient chaos

Z. Kaufmann·A. Németh·P. Szépfalusy
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Abstract

One-dimensional maps exhibiting transient chaos and defined on two preimages of the unit interval [0,1] are investigated. It is shown that such maps have continuously many conditionally invariant measures $μ_σ$ scaling at the fixed point at x=0 as $x^σ$, but smooth elsewhere. Here $σ$ should be smaller than a critical value $σ_{c}$ that is related to the spectral properties of the Frobenius-Perron operator. The corresponding natural measures are proven to be entirely concentrated on the fixed point.

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BibTeXRIS

Z. Kaufmann, A. Németh, P. Szépfalusy. 1999-07-28. Critical states of transient chaos. https://doi.org/10.1103/physreve.61.2543

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