Browsing by Subject "topological degree"

Now showing 1 - 2 of 2
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    Periodic points of latitudinal maps of the m-dimensional sphere
    (AIMS, 2016-11) Graff, Grzegorz; Misiurewicz, Michał; Nowak-Przygodzki, Piotr; Department of Mathematical Sciences, School of Science
    Let f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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    Shub’s conjecture for smooth longitudinal maps of Sm
    (Taylor & Francis, 2018) Graff, Grzegorz; Misiurewicz, Michał; Nowak-Przygodzki, Piotr; Mathematical Sciences, School of Science
    Let f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f, reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m=2 and in a weak form for m=3.