Invariant measures exist without a growth condition
UNSPECIFIED. (2003) Invariant measures exist without a growth condition. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 241 (2-3). pp. 287-306. ISSN 0010-3616Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00220-003-0928-z
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  and Martens & Nowicki  can be weakened considerably.
|Item Type:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Journal or Publication Title:||COMMUNICATIONS IN MATHEMATICAL PHYSICS|
|Number of Pages:||20|
|Page Range:||pp. 287-306|
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