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

Marek R Rychlik, Eugene Sorets

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 1992
Externally publishedYes

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Absolutely Continuous Invariant Measure
regularity
Lyapunov Exponent
Regularity
Exactness
theorems
Theorem
Invariant Measure
Positivity
exponents
Deduce
Uniqueness
Dynamical system
uniqueness
dynamical systems
Family

ASJC Scopus subject areas

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

Cite this

Regularity and other properties of absolutely continuous invariant measures for the quadratic family. / Rychlik, Marek R; Sorets, Eugene.

In: Communications in Mathematical Physics, Vol. 150, No. 2, 11.1992, p. 217-236.

Research output: Contribution to journalArticle

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