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  • 1. Golenishcheva-Kutuzova, Tatiana
    et al.
    Gorodetski, Anton
    Kleptsyn, Victor
    Volk, Denis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Translation numbers define generators of f-k(+) -> Homeo(+) (S-1)2014In: Moscow Mathematical Journal, ISSN 1609-3321, E-ISSN 1609-4514, Vol. 14, no 2, p. 291-308Article in journal (Refereed)
    Abstract [en]

    We consider a minimal action of a finitely generated semigroup by homeomorphisms of the circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random dynamics of circle homeomorphisms: Antonov's theorem and its corollaries.

  • 2.
    Salafia, C.
    et al.
    Placental Analyt LLC, Larchmont, NY 10538 USA.;New York State Inst Basic Res Dev Disabil, Staten Isl, NY 10314 USA..
    Yampolsky, M.
    Univ Toronto, Toronto, ON, Canada..
    Volk, Denis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Stodgell, C. J.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Univ Rochester, Sch Med & Dent, Rochester, NY USA..
    Katzman, P. J.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Univ Rochester, Sch Med & Dent, Rochester, NY USA..
    Culhane, J.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Childrens Hosp Philadelphia, Philadelphia, PA 19104 USA..
    Landrigan, P.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Mt Sinai Sch Med, New York, NY USA..
    Szabo, S.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Med Coll Wisconsin, Milwaukee, WI 53226 USA..
    Thieux, N.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;S Dakota State Univ, Brookings, SD 57007 USA..
    Swanson, J.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Univ Calif Irvine, Irvine, CA USA..
    Dole, N.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Univ N Carolina, Chapel Hill, NC USA..
    Varner, M. W.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Univ Utah, Salt Lake City, UT USA..
    Moye, J.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;NIH, Natl Childrens Study, Bethesda, MD 20892 USA..
    Miller, R.
    Natl Childrens Study Placenta Consortium, Bethesda, MD USA.;Univ Rochester, Sch Med & Dent, Rochester, NY USA..
    Mapping placental topology from 3D scans, the graphic display of variation in arborisation across gestation (vol 34, pg A73, 2013)2014In: Placenta, ISSN 0143-4004, E-ISSN 1532-3102, Vol. 35, no 1, p. 75-75Article in journal (Refereed)
  • 3. Salafia, Carolyn
    et al.
    Yampolsky, Michael
    Volk, Denis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Stodgell, C. J.
    Katzman, P. J.
    Culhane, J.
    Landrigan, P.
    Szabo, S.
    Thieux, N.
    Swanson, J.
    Dole, N.
    Varner, M. W.
    Moye, John
    Miller, Richard
    Mapping Placental Topology From 3d Scans, The Graphic Display Of Variation In Arborisation Across Gestation2013In: Placenta, ISSN 0143-4004, E-ISSN 1532-3102, Vol. 34, no 9, p. A73-A74Article in journal (Other academic)
  • 4.
    Volk, Denis
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Almost every interval translation map of three intervals is finite type2014In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 5, p. 2307-2314Article in journal (Refereed)
    Abstract [en]

    Interval translation maps (ITMs) are a non-invertible generalization of interval exchange transformations (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. In this paper, we prove the finiteness conjecture for the ITMs of three intervals. Namely, the subset of ITMs of finite type contains an open, dense, and full Lebesgue measure subset of the space of ITMs of three intervals. For this, we show that any ITM of three intervals can be reduced either to a rotation or to a double rotation.

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