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Periodic points of latitudinal maps of the $m$-dimensional sphere

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  • Let $f$ be a smooth self-map of the $m$-dimensional sphere $S^m$. Under the assumption that $f$ preserves latitudinal foliations with the fibres $S^1$, 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.
    Mathematics Subject Classification: Primary: 37C25, 37E30, 55M20.


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  • [1]

    I. K. Babenko, S. A. Bogatyi, The behavior of the index of periodic points under iterations of a mapping, Math. USSR Izv., 38 (1992), 1-26.


    G. Graff and J. Jezierski, On the growth of the number of periodic points for smooth self-maps of a compact manifold, Proc. Amer. Math. Soc., 135 (2007), 3249-3254.doi: 10.1090/S0002-9939-07-08836-3.


    L. Hernández-Corbato and F. R. Ruiz del Portal, Fixed point indices of planar continuous maps, Discrete Contin. Dyn. Syst., 35 (2015), 2979-2995.doi: 10.3934/dcds.2015.35.2979.


    B. J. Jiang, Lectures on the Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983.


    V. Kaloshin, Generic diffeomorphisms with superexponential growth of number of periodic orbits, Comm. Math. Phys., 211 (2000), 253-271.doi: 10.1007/s002200050811.


    N. G. Lloyd, Degree Theory, Cambridge Tracts in Mathematics, 73, Cambridge University Press, Cambridge-New York-Melbourne, 1978.


    M. Misiurewicz, Periodic points of latitudinal maps, J. Fixed Point Theory Appl., 16 (2014), 149-158.doi: 10.1007/s11784-014-0195-y.


    C. Pugh and M. Shub, Periodic points on the 2-sphere, Discrete Contin. Dynam. Sys., 34 (2014), 1171-1182.doi: 10.3934/dcds.2014.34.1171.


    M. Shub, Alexander cocycles and dynamics, Asterisque, 51, Societé Math. de France, (1978), 395-413.


    M. Shub, All, most, some differentiable dynamical systems, Proceedings of the International Congress of Mathematicians, Madrid, Spain, (2006), European Math. Society, 99-120.


    M. Shub, Dynamical systems, filtration and entropy, Bull. Amer. Math. Soc., 80 (1974), 27-41.doi: 10.1090/S0002-9904-1974-13344-6.


    M. Shub and P. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps, Topology, 13 (1974), 189-191.doi: 10.1016/0040-9383(74)90009-3.

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