Critical states of transient chaos

Z. Kaufmann, A. Németh, P. Szépfalusy

Research output: Contribution to journalArticle

5 Citations (Scopus)


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 [Formula Presented] scaling at the fixed point at [Formula Presented] as [Formula Presented] but smooth elsewhere. Here, [Formula Presented] should be smaller than a critical value [Formula Presented] that is related to the spectral properties of the Frobenius-Perron operator. The corresponding natural measures are proven to be entirely concentrated in the fixed point.

Original languageEnglish
Pages (from-to)2543-2550
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number3
Publication statusPublished - Jan 1 2000


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)

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