Regularity and other properties of absolutely continuous invariant measures for the quadratic family

Marek Rychlik, Eugene Sorets

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

In the current paper we study in more detail some properties of the absolutely continuous invariant measures constructed in the course of the proof of Jakobson's Theorem. In particular, we show that the density of the invariant measure is continuous at Misiurewicz points. From this we deduce that the Lyapunov exponent is also continuous at these points (our considerations apply just to the parameters constructed in the proof of Jakobson's Theorem). Other properties, like the positivity of the Lyapunov exponent, uniqueness of the absolutely continuous invariant measure and exactness of the corresponding dynamical system, are also proved.

Original languageEnglish (US)
Pages (from-to)217-236
Number of pages20
JournalCommunications in Mathematical Physics
Volume150
Issue number2
DOIs
StatePublished - Nov 1 1992
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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