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  • 1.
    Bränden, Petter
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Wagner, David G.
    A converse to the Grace-Walsh-Szego theorem2009In: Mathematical proceedings of the Cambridge Philosophical Society (Print), ISSN 0305-0041, E-ISSN 1469-8064, Vol. 147, p. 447-453Article in journal (Refereed)
    Abstract [en]

    We prove that the symmetrizer of a permutation group preserves stability if and only if the group is orbit homogeneous. A consequence is that the hypothesis of permutation invariance in the Grace-Walsh-Szego Coincidence Theorem cannot be relaxed. In the process we obtain a new characterization of the Grace-like polynomials, introduced by D. Ruelle, and prove that the class of such polynomials can be endowed with a natural multiplication.

  • 2.
    Dobbs, Neil
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Nice sets and invariant densities in complex dynamics2011In: Mathematical proceedings of the Cambridge Philosophical Society (Print), ISSN 0305-0041, E-ISSN 1469-8064, Vol. 150, p. 157-165Article in journal (Refereed)
    Abstract [en]

    In complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a construction of Rivera-Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and 'Swiatek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.

  • 3. Ringström, Hans
    On Gowdy vacuum spacetimes2004In: Mathematical proceedings of the Cambridge Philosophical Society (Print), ISSN 0305-0041, E-ISSN 1469-8064, Vol. 136, p. 485-512Article in journal (Refereed)
    Abstract [en]

    Using Fuchsian techniques, a large family of Gowdy vacuum spacetimes have been constructed for which one has detailed control over asymptotic behaviour. In this paper we formulate a, condition on initial data yielding the same form of asymptotics.

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