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Whitney-Holder continuity of the SRB measure for transversal families of smooth unimodal maps
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2015 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 201, no 3, 773-844 p.Article in journal (Refereed) Published
Abstract [en]

We consider families of nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure of , as a function of on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming existence of a transversal CE parameter, we find a positive measure set of CE parameters , and, for each , a set of polynomially recurrent parameters containing as a Lebesgue density point, and constants , , so that, for every -Holder function , In addition, for all , the renormalisation period of satisfies , and there are uniform bounds on the rates of mixing of for all with . If , the set contains almost all CE parameters. Lower bounds: Assuming existence of a transversal mixing Misiurewicz-Thurston parameter , we find a set of CE parameters accumulating at , a constant , and a function , so that C vertical bar t - t(0)vertical bar(1/2) >= vertical bar integral A(0)d mu(t) - integral A(0)d mu(t0) vertical bar >= C-1 vertical bar t - t(0)vertical bar(1/2), for all t is an element of Delta(MT)'.

Place, publisher, year, edition, pages
2015. Vol. 201, no 3, 773-844 p.
Keyword [en]
KeyWords Plus:LINEAR-RESPONSE; SUSCEPTIBILITY FUNCTION; STATISTICAL PROPERTIES; STOCHASTIC STABILITY; INVARIANT-MEASURES; DYNAMICAL-SYSTEMS; QUADRATIC FAMILY; DEFORMATIONS; ANALYTICITY; DEPENDENCE
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-173424DOI: 10.1007/s00222-014-0554-8ISI: 000359998900001Scopus ID: 2-s2.0-84939777141OAI: oai:DiVA.org:kth-173424DiVA: diva2:853670
Note

QC 20150914

Available from: 2015-09-14 Created: 2015-09-11 Last updated: 2017-12-04Bibliographically approved

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CiteExportLink to record
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  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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More styles
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  • de-DE
  • en-GB
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  • nn-NB
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Output format
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