Another proof of Jakobson's Theorem and related results

Marek Ryszard Rychlik

doi:10.1017/S014338570000434X

Another proof of Jakobson's Theorem and related results

Marek Ryszard Rychlik

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

43 Scopus citations

Abstract

The author shows that any family C2-close to f_α(x) = 1 − αx2(2 − ε ≤ α ≤ 2) satisfies Jakobson's theorem: For a positive measure set of α the transformation f_α has an absolutely continuous invariant measure. He also indicates some generalizations.

Original language	English (US)
Pages (from-to)	93-109
Number of pages	17
Journal	Ergodic Theory and Dynamical Systems
Volume	8
Issue number	1
DOIs	https://doi.org/10.1017/S014338570000434X
State	Published - Mar 1988
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/S014338570000434X

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title = "Another proof of Jakobson's Theorem and related results",

abstract = "The author shows that any family C2-close to fα(x) = 1 − αx2(2 − ε ≤ α ≤ 2) satisfies Jakobson's theorem: For a positive measure set of α the transformation fα has an absolutely continuous invariant measure. He also indicates some generalizations.",

author = "Rychlik, {Marek Ryszard}",

year = "1988",

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AB - The author shows that any family C2-close to fα(x) = 1 − αx2(2 − ε ≤ α ≤ 2) satisfies Jakobson's theorem: For a positive measure set of α the transformation fα has an absolutely continuous invariant measure. He also indicates some generalizations.

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Another proof of Jakobson's Theorem and related results

Abstract

ASJC Scopus subject areas

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