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Viana maps and limit distributions of sums of point measures
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). (Analysgruppen)
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: US-AB , 2009. , vii, 37 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 09:14
Keyword [en]
Viana maps, absolutely continuous invariant measures, skew-products, quadratic maps, Bernoulli convolutions, absolute continuity, typical points, equidistributed sequences, uniformly distibuted sequences
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-11477ISBN: 978-91-7415-521-1 (print)OAI: oai:DiVA.org:kth-11477DiVA: diva2:279254
Public defence
2009-12-17, Kollegiesalen F3, Kungl Tekniska högskolan, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2009-12-03 Created: 2009-11-16 Last updated: 2012-02-24Bibliographically approved
List of papers
1. Non-continuous weakly expanding skew-products of quadratic maps with two positive Lyapunov exponents
Open this publication in new window or tab >>Non-continuous weakly expanding skew-products of quadratic maps with two positive Lyapunov exponents
2008 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 28, no 1, 245-266 p.Article in journal (Refereed) Published
Abstract [en]

We study an extension of the Viana map where the base dynamics isa discontinuous expanding map, and prove the existence of two positive Lyapunovexponents.

National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-11645 (URN)10.1017/S0143385707000429 (DOI)000253117600010 ()2-s2.0-38149135935 (Scopus ID)
Note
QC 20100809Available from: 2009-12-03 Created: 2009-11-28 Last updated: 2017-12-12Bibliographically approved
2. Positive Lyapunov exponents for quadratic skew-products over  a Misiurewicz-Thurston map
Open this publication in new window or tab >>Positive Lyapunov exponents for quadratic skew-products over  a Misiurewicz-Thurston map
2009 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 22, 2681-2695 p.Article in journal (Refereed) Published
Abstract [en]

We study a class of skew-products of quadratic maps-also called Viana maps-where the base dynamics is given by a high enough iteration of a Misiurewicz-Thurston quadratic map. We show that these systems admit two positive Lyapunov exponents.

National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-11646 (URN)10.1088/0951-7715/22/11/006 (DOI)000270757400006 ()2-s2.0-70350650726 (Scopus ID)
Note
QC 20100809Available from: 2009-12-03 Created: 2009-11-28 Last updated: 2017-12-12Bibliographically approved
3. Almost sure absolute continuity of Bernoulli convolutions
Open this publication in new window or tab >>Almost sure absolute continuity of Bernoulli convolutions
2010 (English)In: Ann. Inst. H. Poincaré Probab. Statist., ISSN 0246-0203, Vol. 46, no 3, 888-893 p.Article in journal (Refereed) Published
Abstract [en]

We prove an extension of a result by Peres and Solomyak on almostsure absolute continuity in a class of symmetric Bernoulli convolutions.

Keyword
Bernoulli convolutions; Absolute continuity
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-11647 (URN)10.1214/09-AIHP334 (DOI)000283528100013 ()2-s2.0-77955640920 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation, KAW 2005.0098
Note
Updated from submitted to published. QC 20120327Available from: 2009-12-03 Created: 2009-11-28 Last updated: 2012-03-27Bibliographically approved
4. Typical points for one-parameter families of piecewise expanding maps of the interval
Open this publication in new window or tab >>Typical points for one-parameter families of piecewise expanding maps of the interval
(English)Manuscript (preprint) (Other (popular science, discussion, etc.))
Identifiers
urn:nbn:se:kth:diva-11648 (URN)
Available from: 2009-12-03 Created: 2009-11-28 Last updated: 2015-11-11

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