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Invariant measures exist without a growth condition
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UNSPECIFIED (2003) Invariant measures exist without a growth condition. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 241 (2-3). pp. 287-306. doi:10.1007/s00220-003-0928-z ISSN 0010-3616.
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Official URL: http://dx.doi.org/10.1007/s00220-003-0928-z
Abstract
Given a non-flat S-unimodal interval map f, we show that there exists C which only depends on the order of the critical point c such that if \Df(n) (f (c))\ greater than or equal to C for all n sufficiently large, then f admits an absolutely continuous invariant probability measure (acip). As part of the proof we show that if the quotients of successive intervals of the principal nest of f are sufficiently small, then f admits an acip. As a special case, any S-unimodal map with critical order l < 2 + ε having no central returns possesses an acip. These results imply that the summability assumptions in the theorems of Nowicki & van Strien [21] and Martens & Nowicki [17] can be weakened considerably.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Journal or Publication Title: | COMMUNICATIONS IN MATHEMATICAL PHYSICS | ||||
Publisher: | SPRINGER-VERLAG | ||||
ISSN: | 0010-3616 | ||||
Official Date: | October 2003 | ||||
Dates: |
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Volume: | 241 | ||||
Number: | 2-3 | ||||
Number of Pages: | 20 | ||||
Page Range: | pp. 287-306 | ||||
DOI: | 10.1007/s00220-003-0928-z | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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