Displaying similar documents to “Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers”

Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers

Grzegorz Graff, Agnieszka Kaczkowska (2013)

Annales Polonici Mathematici

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Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence L ( f ⁿ ) n = 1 ∞ of the Lefschetz numbers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defined in combinatorial terms and is constant for all sufficiently large r. We compute J[f]...