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Quasi-periodic kicking of circle diffeomorphisms having unique fixed points
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)In: Moscow Mathematical Journal, ISSN 1609-3321, E-ISSN 1609-4514, Vol. 19, no 2, p. 189-216Article in journal (Refereed) Published
Abstract [en]

We investigate the dynamics of certain homeomorphisms F: T-2 -> T-2 of the form F(x, y) = (x + omega , h(x)+ f (y)), where omega is an element of R\Q, f: T -> T is a circle diffeomorphism with a unique (and thus neutral) fixed point and h: T -> T is a function which is zero outside a small interval. We show that such a map can display a non-uniformly hyperbolic behavior: (small) negative fibred Lyapunov exponents for a.e. (x, y) and an attracting non-continuous invariant graph. We apply this result to (projective) SL(2, R)-cocycles G: (x, u) bar right arrow (x + omega, A(x)u) with A(x) = R phi(x)B, where R-theta is a rotation matrix and B is a parabolic matrix, to get exam ples of non-uniformly hyperbolic cocycles (homotopic to the identity) with perturbatively small Lyapunov exponents.

Place, publisher, year, edition, pages
Independent University of Moscow , 2019. Vol. 19, no 2, p. 189-216
Keywords [en]
Lyapunov exponents, quasi-periodic forcing, non-uniform hyperbolicity, cocycles
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-255587DOI: 10.17323/1609-4514-2019-19-2-189-216ISI: 000475756300002Scopus ID: 2-s2.0-85067058396OAI: oai:DiVA.org:kth-255587DiVA, id: diva2:1340486
Note

QC 20190805

Available from: 2019-08-05 Created: 2019-08-05 Last updated: 2019-08-05Bibliographically approved

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Bjerklöv, Kristian

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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